From 49f77110d6603f885e71864524db293bad323a5f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 10:22:50 +0100
Subject: [PATCH 01/56] Initial commit

---
 .gitignore | 9 +++++++++
 1 file changed, 9 insertions(+)
 create mode 100644 .gitignore

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 000000000..1127ecefb
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,9 @@
+*~
+*.mat
+*.eps
+*.fig
+*.pdf
+*.log
+*.tex
+*_dynamic.m
+*_static.m

From 6d6bffe9aa3aa806778cabcd03029c414a63762b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 10:23:58 +0100
Subject: [PATCH 02/56] Added VAR model example.

---
 examples/var/m1.mod | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 examples/var/m1.mod

diff --git a/examples/var/m1.mod b/examples/var/m1.mod
new file mode 100644
index 000000000..9f0eb32d1
--- /dev/null
+++ b/examples/var/m1.mod
@@ -0,0 +1,30 @@
+var x y z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 c_z_1 d;
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2; 
+c_z_1 =  .9;
+d     =  .1;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*x(-1) + b_y_1*y(-2) + b_y_2*x(-2) + ey ;
+
+z = c_z_1*z(-3) + d*y + ez;
+
+[name='eq:x']
+x = b_x_1*y(-2) + b_x_2*x(-2) + ez ;
+
+end;
+
+get_ar_matrices('toto');

From b03edd8082493bf26d11d0757597005c7459366c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 11:24:34 +0100
Subject: [PATCH 03/56] Changed variables ordering in example.

---
 examples/var/m1.mod | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/var/m1.mod b/examples/var/m1.mod
index 9f0eb32d1..698c82fa5 100644
--- a/examples/var/m1.mod
+++ b/examples/var/m1.mod
@@ -1,4 +1,4 @@
-var x y z;
+var y x z;
 
 varexo ex ey ez;
 
@@ -27,4 +27,4 @@ x = b_x_1*y(-2) + b_x_2*x(-2) + ez ;
 
 end;
 
-get_ar_matrices('toto');
+get_companion_matrix('toto');

From 7dbf407af33d056c9065cda07e567513db2db619 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 11:24:54 +0100
Subject: [PATCH 04/56] Added shell script.

---
 examples/var/clean | 4 ++++
 1 file changed, 4 insertions(+)
 create mode 100755 examples/var/clean

diff --git a/examples/var/clean b/examples/var/clean
new file mode 100755
index 000000000..2f60f0223
--- /dev/null
+++ b/examples/var/clean
@@ -0,0 +1,4 @@
+#!/bin/sh
+
+rm -rf m1
+rm -f m1_dynamic.m  m1.log  m1.m  m1_results.mat  m1_set_auxiliary_variables.m  m1_static.m
\ No newline at end of file

From 21a2f28c0e125e48600e14f0e6679d29687afab5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 11:27:17 +0100
Subject: [PATCH 05/56] Fixed encoding.

---
 examples/var/m1.mod | 60 ++++++++++++++++++++++-----------------------
 1 file changed, 30 insertions(+), 30 deletions(-)

diff --git a/examples/var/m1.mod b/examples/var/m1.mod
index 698c82fa5..7ebe59034 100644
--- a/examples/var/m1.mod
+++ b/examples/var/m1.mod
@@ -1,30 +1,30 @@
-var y x z;
-
-varexo ex ey ez;
-
-parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 c_z_1 d;
-
-a_y_1 =  .2;
-a_y_2 =  .3;
-b_y_1 =  .1;
-b_y_2 =  .4;
-b_x_1 = -.1;
-b_x_2 = -.2; 
-c_z_1 =  .9;
-d     =  .1;
-
-var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
-
-model;
-
-[name='eq:y']
-y = a_y_1*y(-1) + a_y_2*x(-1) + b_y_1*y(-2) + b_y_2*x(-2) + ey ;
-
-z = c_z_1*z(-3) + d*y + ez;
-
-[name='eq:x']
-x = b_x_1*y(-2) + b_x_2*x(-2) + ez ;
-
-end;
-
-get_companion_matrix('toto');
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 c_z_1 d;
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2; 
+c_z_1 =  .9;
+d     =  .1;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*x(-1) + b_y_1*y(-2) + b_y_2*x(-2) + ey ;
+
+z = c_z_1*z(-3) + d*y + ez;
+
+[name='eq:x']
+x = b_x_1*y(-2) + b_x_2*x(-2) + ez ;
+
+end;
+
+get_companion_matrix('toto');

From ab1c24d853fa1adb034e94c1bc25d8711435e2dc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 11:47:10 +0100
Subject: [PATCH 06/56] Added VAR example with diff.

---
 examples/var/clean  |  5 +++--
 examples/var/m2.mod | 30 ++++++++++++++++++++++++++++++
 2 files changed, 33 insertions(+), 2 deletions(-)
 create mode 100644 examples/var/m2.mod

diff --git a/examples/var/clean b/examples/var/clean
index 2f60f0223..d09a225cc 100755
--- a/examples/var/clean
+++ b/examples/var/clean
@@ -1,4 +1,5 @@
 #!/bin/sh
 
-rm -rf m1
-rm -f m1_dynamic.m  m1.log  m1.m  m1_results.mat  m1_set_auxiliary_variables.m  m1_static.m
\ No newline at end of file
+rm -rf m1 m2
+rm -f m1_dynamic.m  m1.log  m1.m  m1_results.mat  m1_set_auxiliary_variables.m  m1_static.m
+rm -f m2_dynamic.m  m2.log  m2.m  m2_results.mat  m2_set_auxiliary_variables.m  m2_static.m
\ No newline at end of file
diff --git a/examples/var/m2.mod b/examples/var/m2.mod
new file mode 100644
index 000000000..475a52039
--- /dev/null
+++ b/examples/var/m2.mod
@@ -0,0 +1,30 @@
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 c_z_1 d;
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2; 
+c_z_1 =  .9;
+d     =  .1;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+z = c_z_1*z(-3) + d*y + ez;
+
+[name='eq:x']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ez ;
+
+end;
+
+get_companion_matrix('toto');
\ No newline at end of file

From 949387c82b84b8248654cb323a1a702674d4bb84 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 15:15:55 +0100
Subject: [PATCH 07/56] Added a model with VAR and PAC equation.

---
 examples/1/clean       |  5 +++++
 examples/1/example.mod | 39 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 44 insertions(+)
 create mode 100755 examples/1/clean
 create mode 100644 examples/1/example.mod

diff --git a/examples/1/clean b/examples/1/clean
new file mode 100755
index 000000000..3cae8a7a8
--- /dev/null
+++ b/examples/1/clean
@@ -0,0 +1,5 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
diff --git a/examples/1/example.mod b/examples/1/example.mod
new file mode 100644
index 000000000..2c51d8e7e
--- /dev/null
+++ b/examples/1/example.mod
@@ -0,0 +1,39 @@
+// --+ options: json=compute +--
+
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
+
+parameters beta g e_c_m c_z_1 c_z_2;               // PAC equation parameters
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2; 
+
+g = .0;
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ez ;
+
+[name='eq:pac']
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
+
+end;
+
+get_companion_matrix('toto');
\ No newline at end of file

From 488913a092589e7ffe3ed87655c3ca94d74dbc3e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 15:52:09 +0100
Subject: [PATCH 08/56] Added VAR model with ECM component.

---
 examples/var/clean  |  5 +++--
 examples/var/m3.mod | 32 ++++++++++++++++++++++++++++++++
 2 files changed, 35 insertions(+), 2 deletions(-)
 create mode 100644 examples/var/m3.mod

diff --git a/examples/var/clean b/examples/var/clean
index d09a225cc..1ac7e3d6a 100755
--- a/examples/var/clean
+++ b/examples/var/clean
@@ -1,5 +1,6 @@
 #!/bin/sh
 
-rm -rf m1 m2
+rm -rf m1 m2 m3
 rm -f m1_dynamic.m  m1.log  m1.m  m1_results.mat  m1_set_auxiliary_variables.m  m1_static.m
-rm -f m2_dynamic.m  m2.log  m2.m  m2_results.mat  m2_set_auxiliary_variables.m  m2_static.m
\ No newline at end of file
+rm -f m2_dynamic.m  m2.log  m2.m  m2_results.mat  m2_set_auxiliary_variables.m  m2_static.m
+rm -f m3_dynamic.m  m3.log  m3.m  m3_results.mat  m3_set_auxiliary_variables.m  m3_static.m
diff --git a/examples/var/m3.mod b/examples/var/m3.mod
new file mode 100644
index 000000000..eaf79b782
--- /dev/null
+++ b/examples/var/m3.mod
@@ -0,0 +1,32 @@
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 c_z_1 c_z_2 c_z_3;
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2; 
+c_z_1 =  .9;
+c_z_2 =  .1;
+c_z_3 = -.8;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y', 'eq:z']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
+
+[name='eq:z']
+diff(z) = c_z_1*(x(-1)-z(-1)) + c_z_2*diff(z(-1)) + c_z_3*diff(z(-2)) + ez ;
+
+end;
+
+get_ar_matrices('toto');
\ No newline at end of file

From 2e0fd8185a48d26a9eaf01ba07fc2579dca4ac34 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 16:53:43 +0100
Subject: [PATCH 09/56] Fixed typo.

---
 examples/1/example.mod | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index 2c51d8e7e..096a623fa 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -13,7 +13,7 @@ a_y_2 =  .3;
 b_y_1 =  .1;
 b_y_2 =  .4;
 b_x_1 = -.1;
-b_x_2 = -.2; 
+b_x_2 = -.2;
 
 g = .0;
 beta  =  .9;
@@ -29,7 +29,7 @@ model;
 y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 
 [name='eq:x']
-diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ez ;
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
 diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;

From f5372bd4ecaf9e2c4ff010acd139db1091c906a5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 16:55:32 +0100
Subject: [PATCH 10/56] Fixed encoding.

---
 examples/1/example.mod | 76 +++++++++++++++++++++---------------------
 1 file changed, 38 insertions(+), 38 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index 096a623fa..dca2e4547 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -1,39 +1,39 @@
-// --+ options: json=compute +--
-
-var y x z;
-
-varexo ex ey ez;
-
-parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
-
-parameters beta g e_c_m c_z_1 c_z_2;               // PAC equation parameters
-
-a_y_1 =  .2;
-a_y_2 =  .3;
-b_y_1 =  .1;
-b_y_2 =  .4;
-b_x_1 = -.1;
-b_x_2 = -.2;
-
-g = .0;
-beta  =  .9;
-e_c_m =  .1;
-c_z_1 =  .7;
-c_z_2 = -.3;
-
-var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
-
-model;
-
-[name='eq:y']
-y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
-
-[name='eq:x']
-diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
-
-[name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
-
-end;
-
+// --+ options: json=compute +--
+
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
+
+parameters beta g e_c_m c_z_1 c_z_2;             // PAC equation parameters
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2;
+
+g = .0;
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
+
+[name='eq:pac']
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
+
+end;
+
 get_companion_matrix('toto');
\ No newline at end of file

From 51a4cb151dd054d18510f61933a1dac6a74f5a70 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 17:12:41 +0100
Subject: [PATCH 11/56] Updated .gitignore file.

---
 .gitignore | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/.gitignore b/.gitignore
index 1127ecefb..7f69f328c 100644
--- a/.gitignore
+++ b/.gitignore
@@ -7,3 +7,8 @@
 *.tex
 *_dynamic.m
 *_static.m
+
+*.m
+*.json
+
+checksum

From 39476809325bebe3db35e4a40f0fc6bdc60da07b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 18:53:28 +0100
Subject: [PATCH 12/56] Added VAR model.

---
 examples/var/clean  |  3 ++-
 examples/var/m4.mod | 29 +++++++++++++++++++++++++++++
 2 files changed, 31 insertions(+), 1 deletion(-)
 create mode 100644 examples/var/m4.mod

diff --git a/examples/var/clean b/examples/var/clean
index 1ac7e3d6a..e0d1cd114 100755
--- a/examples/var/clean
+++ b/examples/var/clean
@@ -1,6 +1,7 @@
 #!/bin/sh
 
-rm -rf m1 m2 m3
+rm -rf m1 m2 m3 m4
 rm -f m1_dynamic.m  m1.log  m1.m  m1_results.mat  m1_set_auxiliary_variables.m  m1_static.m
 rm -f m2_dynamic.m  m2.log  m2.m  m2_results.mat  m2_set_auxiliary_variables.m  m2_static.m
 rm -f m3_dynamic.m  m3.log  m3.m  m3_results.mat  m3_set_auxiliary_variables.m  m3_static.m
+rm -f m4_dynamic.m  m4.log  m4.m  m4_results.mat  m4_set_auxiliary_variables.m  m4_static.m
diff --git a/examples/var/m4.mod b/examples/var/m4.mod
new file mode 100644
index 000000000..f92fc75ed
--- /dev/null
+++ b/examples/var/m4.mod
@@ -0,0 +1,29 @@
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_x_0 a_x_1 a_x_2 b_z_0 b_z_1 b_z_2;
+
+a_x_0 =  .2;
+a_x_1 =  .9;
+a_x_2 = -.2;
+b_z_0 =  .3;
+b_z_1 =  .7;
+b_z_2 = -.4;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:z', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = y(-1) + ey ;
+
+[name='eq:x']
+diff(x) = -a_x_0*(x(-1)-y(-1)) + a_x_1*diff(x(-1)) + a_x_2*diff(x(-2)) + ex ;
+
+[name='eq:z']
+diff(z) = -b_z_0*(z(-1)-x(-1)) + b_z_1*diff(z(-1)) + b_z_2*diff(z(-2)) + ez ;
+
+end;
+
+get_ar_matrices('toto');
\ No newline at end of file

From 4ccb810530afd18a99f316e092fd70c919d957ff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 9 Feb 2018 18:54:08 +0100
Subject: [PATCH 13/56] Fixed non complete cleanup.

---
 examples/1/clean | 1 +
 1 file changed, 1 insertion(+)

diff --git a/examples/1/clean b/examples/1/clean
index 3cae8a7a8..2f26c4b7a 100755
--- a/examples/1/clean
+++ b/examples/1/clean
@@ -3,3 +3,4 @@
 rm -rf example
 rm -f example_dynamic.json example.json example.m example_original.json example_static.json
 rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_results.mat

From b1368c4e851ae38ba97d2241da2987dacd398ec0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 15 Feb 2018 15:23:23 +0100
Subject: [PATCH 14/56] Updated first pac model example.

---
 examples/1/example.mod | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index dca2e4547..586443079 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -6,7 +6,7 @@ varexo ex ey ez;
 
 parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
 
-parameters beta g e_c_m c_z_1 c_z_2;             // PAC equation parameters
+parameters beta e_c_m c_z_1 c_z_2;               // PAC equation parameters
 
 a_y_1 =  .2;
 a_y_2 =  .3;
@@ -15,7 +15,6 @@ b_y_2 =  .4;
 b_x_1 = -.1;
 b_x_2 = -.2;
 
-g = .0;
 beta  =  .9;
 e_c_m =  .1;
 c_z_1 =  .7;
@@ -28,11 +27,11 @@ model;
 [name='eq:y']
 y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 
-[name='eq:x']
+[name='eq:x', data_type='nonstationary']
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta) + ez;
 
 end;
 

From 9f02392ee6c7317ac0c1366202a62e0731cf4289 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 15 Feb 2018 15:34:57 +0100
Subject: [PATCH 15/56] Added more PAC model examples.

---
 examples/2/example.mod | 40 ++++++++++++++++++++++++++++++++++++++++
 examples/3/example.mod | 38 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 78 insertions(+)
 create mode 100644 examples/2/example.mod
 create mode 100644 examples/3/example.mod

diff --git a/examples/2/example.mod b/examples/2/example.mod
new file mode 100644
index 000000000..72ca27ae0
--- /dev/null
+++ b/examples/2/example.mod
@@ -0,0 +1,40 @@
+// --+ options: json=compute +--
+
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 gamma; // VAR parameters
+
+parameters beta e_c_m c_z_1 c_z_2;               // PAC equation parameters
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2;
+
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x', data_type='nonstationary']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta)) + (1-gamma)*ez;
+
+end;
+
+get_companion_matrix('toto');
\ No newline at end of file
diff --git a/examples/3/example.mod b/examples/3/example.mod
new file mode 100644
index 000000000..4e5b44640
--- /dev/null
+++ b/examples/3/example.mod
@@ -0,0 +1,38 @@
+// --+ options: json=compute +--
+
+var y x z;
+
+varexo ex ey ez g;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
+
+parameters beta e_c_m c_z_1 c_z_2;               // PAC equation parameters
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2;
+
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x', data_type='nonstationary']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
+
+[name='eq:pac']
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
+
+end;
+
+get_companion_matrix('toto');

From d09268e2ab42ae5c8fe8d5bb812a6798c7a467f0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Tue, 10 Apr 2018 14:47:34 +0200
Subject: [PATCH 16/56] Adapted mod files for new PAC interface.

---
 examples/1/clean       |  1 +
 examples/1/example.mod |  4 +++-
 examples/2/clean       |  7 +++++++
 examples/2/example.mod | 25 ++++++++++++++++++++++---
 examples/3/clean       |  7 +++++++
 examples/3/example.mod |  8 ++++++--
 6 files changed, 46 insertions(+), 6 deletions(-)
 create mode 100755 examples/2/clean
 create mode 100644 examples/3/clean

diff --git a/examples/1/clean b/examples/1/clean
index 2f26c4b7a..891616064 100755
--- a/examples/1/clean
+++ b/examples/1/clean
@@ -3,4 +3,5 @@
 rm -rf example
 rm -f example_dynamic.json example.json example.m example_original.json example_static.json
 rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
 rm -f example_results.mat
diff --git a/examples/1/example.mod b/examples/1/example.mod
index 586443079..106e52227 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -22,6 +22,8 @@ c_z_2 = -.3;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
+pac_model(var_model_name=toto, discount=beta, model_name=pacman);
+
 model;
 
 [name='eq:y']
@@ -31,7 +33,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/examples/2/clean b/examples/2/clean
new file mode 100755
index 000000000..891616064
--- /dev/null
+++ b/examples/2/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat
diff --git a/examples/2/example.mod b/examples/2/example.mod
index 72ca27ae0..9e99f2994 100644
--- a/examples/2/example.mod
+++ b/examples/2/example.mod
@@ -1,6 +1,6 @@
 // --+ options: json=compute +--
 
-var y x z;
+var y x z ;
 
 varexo ex ey ez;
 
@@ -24,6 +24,8 @@ gamma =  .7;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
+pac_model(var_model_name=toto, discount=beta, model_name=pacman);
+
 model;
 
 [name='eq:y']
@@ -33,8 +35,25 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
-get_companion_matrix('toto');
\ No newline at end of file
+shocks;
+    var ey = 1.0;
+    var ex = 1.0;
+    var ez = 1.0;
+end;
+
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file
diff --git a/examples/3/clean b/examples/3/clean
new file mode 100644
index 000000000..891616064
--- /dev/null
+++ b/examples/3/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat
diff --git a/examples/3/example.mod b/examples/3/example.mod
index 4e5b44640..30030541b 100644
--- a/examples/3/example.mod
+++ b/examples/3/example.mod
@@ -2,9 +2,9 @@
 
 var y x z;
 
-varexo ex ey ez g;
+varexo ex ey ez ;
 
-parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 g; // VAR parameters
 
 parameters beta e_c_m c_z_1 c_z_2;               // PAC equation parameters
 
@@ -20,8 +20,12 @@ e_c_m =  .1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
+g = .02;
+
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
+
+
 model;
 
 [name='eq:y']

From 3f68c5d0e5e3c3d6eba6ff221e5f744e451b4844 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Sun, 15 Apr 2018 21:45:46 +0200
Subject: [PATCH 17/56] added example (with VECM).

---
 examples/4/clean       |  7 ++++
 examples/4/example.mod | 72 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 79 insertions(+)
 create mode 100755 examples/4/clean
 create mode 100644 examples/4/example.mod

diff --git a/examples/4/clean b/examples/4/clean
new file mode 100755
index 000000000..891616064
--- /dev/null
+++ b/examples/4/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat
diff --git a/examples/4/example.mod b/examples/4/example.mod
new file mode 100644
index 000000000..e563d79c9
--- /dev/null
+++ b/examples/4/example.mod
@@ -0,0 +1,72 @@
+// --+ options: json=compute +--
+
+var x1 x2 x1bar x2bar z ;
+
+varexo ex1 ex2 ex1bar ex2bar ez ;
+
+parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+a_x1_0 = -.3;
+a_x1_1 =  .3;
+a_x1_2 =  .1;
+a_x1_x2_1 =  .1;
+a_x1_x2_2 = -.2;
+
+
+a_x2_0 = -.9;
+a_x2_1 =  .2;
+a_x2_2 = -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = -.3;
+
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file

From 1984d01d2ae60022b87feb4a81cf489c0d4c6f2f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 17 May 2018 11:53:01 +0200
Subject: [PATCH 18/56] Updated example for new PAC model interface.

---
 examples/3/example.mod | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/3/example.mod b/examples/3/example.mod
index 30030541b..e0f2fe1b7 100644
--- a/examples/3/example.mod
+++ b/examples/3/example.mod
@@ -24,7 +24,7 @@ g = .02;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
-
+pac_model(var_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(model_name=pacman, var_model_name=toto, discount=beta, growth=g) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 

From 6564e4201cf1791fd3c0accf7ec1a524ba2dd995 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 31 May 2018 13:41:27 +0200
Subject: [PATCH 19/56] Updated examples.

---
 examples/1/example.mod | 17 ++++++++++++++++-
 examples/2/example.mod |  2 +-
 examples/3/example.mod | 18 +++++++++++++++++-
 3 files changed, 34 insertions(+), 3 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index 106e52227..dce8c7146 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -37,4 +37,19 @@ diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_exp
 
 end;
 
-get_companion_matrix('toto');
\ No newline at end of file
+shocks;
+    var ex = 1.0;
+    var ey = 1.0;
+    var ez = 1.0;
+end;
+
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file
diff --git a/examples/2/example.mod b/examples/2/example.mod
index 9e99f2994..eb295a4bd 100644
--- a/examples/2/example.mod
+++ b/examples/2/example.mod
@@ -47,7 +47,7 @@ end;
 
 
 // Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto');
+get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.equation('pacman');
diff --git a/examples/3/example.mod b/examples/3/example.mod
index e0f2fe1b7..c7f2f6fb0 100644
--- a/examples/3/example.mod
+++ b/examples/3/example.mod
@@ -39,4 +39,20 @@ diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_exp
 
 end;
 
-get_companion_matrix('toto');
+shocks;
+    var ey = 1.0;
+    var ex = 1.0;
+    var ez = 1.0;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file

From 9f00a1573ebaeff5c5f29b3a4f7f57c8a01eb4d8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 31 May 2018 13:42:44 +0200
Subject: [PATCH 20/56] Changed calibration.

---
 examples/4/example.mod | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/examples/4/example.mod b/examples/4/example.mod
index e563d79c9..8d5d0adba 100644
--- a/examples/4/example.mod
+++ b/examples/4/example.mod
@@ -8,27 +8,27 @@ parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
 	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
 	   e_c_m c_z_1 c_z_2 gamma beta ;
 
-a_x1_0 = -.3;
-a_x1_1 =  .3;
-a_x1_2 =  .1;
-a_x1_x2_1 =  .1;
-a_x1_x2_2 = -.2;
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
 
 
-a_x2_0 = -.9;
-a_x2_1 =  .2;
-a_x2_2 = -.1;
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
 a_x2_x1_1 = -.1;
-a_x2_x1_2 = -.3;
+a_x2_x1_2 = .2;
 
-beta  =  .9;
-e_c_m =  .1;
-c_z_1 =  .7;
-c_z_2 = -.3;
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+var_model(model_name=toto, eqtags=[  'eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
 
 pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
 
@@ -60,7 +60,7 @@ shocks;
 end;
 
 // Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto');
+get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.equation('pacman');

From 1d0a2ae7a303dc65809c48f61165a9f36cc0496f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 31 May 2018 13:43:26 +0200
Subject: [PATCH 21/56] Added example (VECM with double differences).

---
 examples/5/example.mod | 74 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)
 create mode 100644 examples/5/example.mod

diff --git a/examples/5/example.mod b/examples/5/example.mod
new file mode 100644
index 000000000..bd26c3886
--- /dev/null
+++ b/examples/5/example.mod
@@ -0,0 +1,74 @@
+// --+ options: json=compute +--
+
+var x1 x2 x1bar x2bar z ;
+
+varexo ex1 ex2 ex1bar ex2bar ez ;
+
+parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .1;
+e_c_m =  .1;
+c_z_1 =  .07;
+c_z_2 = -.3;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:x1', data_type='nonstationary']
+diff(diff(x1)) = a_x1_0*(diff(x1(-1))-diff(x1bar(-1))) + a_x1_1*diff(diff(x1(-1))) + a_x1_2*diff(diff(x1(-2))) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(diff(x1(-1))) + a_x2_2*diff(diff(x1(-2))) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+diff(x1bar) = diff(x1bar(-1)) + ex1bar;
+
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file

From 41154f8dffbc2b798777e62ffd3379e3efdd5366 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 1 Jun 2018 14:12:54 +0200
Subject: [PATCH 22/56] Added model with log under diff operator.

---
 examples/6/example.mod | 75 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 examples/6/example.mod

diff --git a/examples/6/example.mod b/examples/6/example.mod
new file mode 100644
index 000000000..88a424cc1
--- /dev/null
+++ b/examples/6/example.mod
@@ -0,0 +1,75 @@
+// --+ options: json=compute +--
+
+var x1 x2 x1bar x2bar z ;
+
+varexo ex1 ex2 ex1bar ex2bar ez ;
+
+parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .1;
+e_c_m =  .1;
+c_z_1 =  .07;
+c_z_2 = -.3;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:x1', data_type='nonstationary']
+diff(diff(x1)) = a_x1_0*(diff(x1(-1))-diff(x1bar(-1))) + a_x1_1*diff(diff(x1(-1))) + a_x1_2*diff(diff(x1(-2))) + a_x1_x2_1*diff(log(x2(-1))) + a_x1_x2_2*diff(log(x2(-2))) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(log(x2)) = a_x2_0*(log(x2(-1))-log(x2bar(-1))) + a_x2_1*diff(diff(x1(-1))) + a_x2_2*diff(diff(x1(-2))) + a_x2_x1_1*diff(log(x2(-1))) + a_x2_x1_2*diff(log(x2(-2))) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+diff(x1bar) = diff(x1bar(-1)) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+log(x2bar) = log(x2bar(-1)) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = .1;
+    var ex1bar = 1.0;
+    var ex2bar = 0.1;
+    var ez = 1.0;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+return
+// Set initial conditions to zero for non logged variables, and one for logged variables
+init = zeros(10, M_.endo_nbr+M_.exo_nbr);
+init(:,[2,4]) = ones(10,2);
+initialconditions = dseries(init, 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file

From c556766ea85f50804848c6106c7c29f1509b6691 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 4 Jun 2018 14:25:45 +0200
Subject: [PATCH 23/56] Changed calibration of innovations and removed return
 statement.

---
 examples/6/example.mod | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/examples/6/example.mod b/examples/6/example.mod
index 88a424cc1..726fed2ae 100644
--- a/examples/6/example.mod
+++ b/examples/6/example.mod
@@ -53,11 +53,11 @@ diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) +
 end;
 
 shocks;
-    var ex1 = 1.0;
-    var ex2 = .1;
-    var ex1bar = 1.0;
-    var ex2bar = 0.1;
-    var ez = 1.0;
+    var ex1 = 1;
+    var ex2 = 1;
+    var ex1bar = 1;
+    var ex2bar = 1;
+    var ez = 1;
 end;
 
 // Build the companion matrix of the VAR model (toto).
@@ -65,7 +65,7 @@ get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.equation('pacman');
-return
+
 // Set initial conditions to zero for non logged variables, and one for logged variables
 init = zeros(10, M_.endo_nbr+M_.exo_nbr);
 init(:,[2,4]) = ones(10,2);

From 285691bd76656e315bf0bc5d080d82668f6adac2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 4 Jun 2018 14:26:42 +0200
Subject: [PATCH 24/56] Added cleanup scripts

---
 examples/5/clean | 7 +++++++
 examples/6/clean | 7 +++++++
 2 files changed, 14 insertions(+)
 create mode 100755 examples/5/clean
 create mode 100755 examples/6/clean

diff --git a/examples/5/clean b/examples/5/clean
new file mode 100755
index 000000000..891616064
--- /dev/null
+++ b/examples/5/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat
diff --git a/examples/6/clean b/examples/6/clean
new file mode 100755
index 000000000..891616064
--- /dev/null
+++ b/examples/6/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat

From 2cd7d305a328ac02708acb18308726e84061cebb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 4 Jun 2018 14:28:31 +0200
Subject: [PATCH 25/56] Fixed permissions.

---
 examples/3/clean | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 mode change 100644 => 100755 examples/3/clean

diff --git a/examples/3/clean b/examples/3/clean
old mode 100644
new mode 100755

From d2249fea4fb51dbb3379b521a9f78fcb63200190 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 4 Jun 2018 14:31:49 +0200
Subject: [PATCH 26/56] Added missing preprocessor option.

---
 examples/6/example.mod | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/6/example.mod b/examples/6/example.mod
index 726fed2ae..c4aa99c00 100644
--- a/examples/6/example.mod
+++ b/examples/6/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, transform_unary_ops +--
 
 var x1 x2 x1bar x2bar z ;
 

From c8ab50e57f583d66310f0d75eadb139af3e13f56 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 4 Jun 2018 14:46:41 +0200
Subject: [PATCH 27/56] Added missing option.

---
 examples/1/example.mod | 2 +-
 examples/2/example.mod | 2 +-
 examples/3/example.mod | 2 +-
 examples/4/example.mod | 2 +-
 examples/5/example.mod | 2 +-
 examples/6/example.mod | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index dce8c7146..d3c136283 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, stochastic +--
 
 var y x z;
 
diff --git a/examples/2/example.mod b/examples/2/example.mod
index eb295a4bd..ae812a28d 100644
--- a/examples/2/example.mod
+++ b/examples/2/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, stochastic +--
 
 var y x z ;
 
diff --git a/examples/3/example.mod b/examples/3/example.mod
index c7f2f6fb0..21ef105b7 100644
--- a/examples/3/example.mod
+++ b/examples/3/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, stochastic +--
 
 var y x z;
 
diff --git a/examples/4/example.mod b/examples/4/example.mod
index 8d5d0adba..87a2524ab 100644
--- a/examples/4/example.mod
+++ b/examples/4/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, stochastic +--
 
 var x1 x2 x1bar x2bar z ;
 
diff --git a/examples/5/example.mod b/examples/5/example.mod
index bd26c3886..66917e0b3 100644
--- a/examples/5/example.mod
+++ b/examples/5/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute +--
+// --+ options: json=compute, stochastic +--
 
 var x1 x2 x1bar x2bar z ;
 
diff --git a/examples/6/example.mod b/examples/6/example.mod
index c4aa99c00..dd207f50b 100644
--- a/examples/6/example.mod
+++ b/examples/6/example.mod
@@ -1,4 +1,4 @@
-// --+ options: json=compute, transform_unary_ops +--
+// --+ options: json=compute, transform_unary_ops, stochastic +--
 
 var x1 x2 x1bar x2bar z ;
 

From 0961e606d5cd0bfde4aa422d22b6ed6490c4c322 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 8 Jun 2018 12:12:47 +0200
Subject: [PATCH 28/56] Added new example with non diagonal A0 EC matrix.

---
 examples/7/clean       |  7 ++++
 examples/7/example.mod | 73 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 80 insertions(+)
 create mode 100755 examples/7/clean
 create mode 100644 examples/7/example.mod

diff --git a/examples/7/clean b/examples/7/clean
new file mode 100755
index 000000000..891616064
--- /dev/null
+++ b/examples/7/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm -f example_dynamic.json example.json example.m example_original.json example_static.json
+rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
+rm -f example_dynamic_set_auxiliary_series.m
+rm -f example_results.mat
diff --git a/examples/7/example.mod b/examples/7/example.mod
new file mode 100644
index 000000000..c090a8140
--- /dev/null
+++ b/examples/7/example.mod
@@ -0,0 +1,73 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z ;
+
+varexo ex1 ex2 ex1bar ex2bar ez ;
+
+parameters a_x1_0 a_x1_0_ a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+a_x1_0 =  -.9;
+a_x1_0_ =  -.8;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+gamma =  .9;
+
+var_model(model_name=toto, eqtags=[  'eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1))+a_x1_0_*(x2(-1)-x2bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 5000);
\ No newline at end of file

From fc925895d7c7f06bd3a82a0ca76ec45993676bed Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 11 Jun 2018 18:24:45 +0200
Subject: [PATCH 29/56] Updated cleanup shell script.

---
 examples/1/clean | 8 ++++----
 examples/2/clean | 8 ++++----
 examples/3/clean | 8 ++++----
 examples/4/clean | 8 ++++----
 examples/5/clean | 8 ++++----
 examples/6/clean | 8 ++++----
 examples/7/clean | 8 ++++----
 7 files changed, 28 insertions(+), 28 deletions(-)

diff --git a/examples/1/clean b/examples/1/clean
index 891616064..19ca1948b 100755
--- a/examples/1/clean
+++ b/examples/1/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/2/clean b/examples/2/clean
index 891616064..19ca1948b 100755
--- a/examples/2/clean
+++ b/examples/2/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/3/clean b/examples/3/clean
index 891616064..19ca1948b 100755
--- a/examples/3/clean
+++ b/examples/3/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/4/clean b/examples/4/clean
index 891616064..19ca1948b 100755
--- a/examples/4/clean
+++ b/examples/4/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/5/clean b/examples/5/clean
index 891616064..19ca1948b 100755
--- a/examples/5/clean
+++ b/examples/5/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/6/clean b/examples/6/clean
index 891616064..19ca1948b 100755
--- a/examples/6/clean
+++ b/examples/6/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/7/clean b/examples/7/clean
index 891616064..19ca1948b 100755
--- a/examples/7/clean
+++ b/examples/7/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm -f example_dynamic.json example.json example.m example_original.json example_static.json
-rm -f example_dynamic.m example.log example_set_auxiliary_variables.m example_static.m
-rm -f example_dynamic_set_auxiliary_series.m
-rm -f example_results.mat
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file

From deec7ca583b04380bb1f85fadf7b9e259f7b1d40 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Tue, 19 Jun 2018 14:05:34 +0200
Subject: [PATCH 30/56] Added new example.

This example allows to test that:

1. the routines are working as expected if the VAR equations are
preceeded by other equations.

2. the simulation algorithm is working if the PAC equation is
augmented by an endogenous variables (exogenous wrt the auxiliary
model model).
---
 examples/8/clean       |  7 ++++
 examples/8/example.mod | 82 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 89 insertions(+)
 create mode 100755 examples/8/clean
 create mode 100644 examples/8/example.mod

diff --git a/examples/8/clean b/examples/8/clean
new file mode 100755
index 000000000..19ca1948b
--- /dev/null
+++ b/examples/8/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/8/example.mod b/examples/8/example.mod
new file mode 100644
index 000000000..ce35414ba
--- /dev/null
+++ b/examples/8/example.mod
@@ -0,0 +1,82 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.equation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
+

From b0f4ecd6b922d1f515150e6781443d6e10be6ae1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 21 Jun 2018 18:52:06 +0200
Subject: [PATCH 31/56] Update examples for deprecated pac.update.equation()
 function.

---
 examples/1/example.mod | 2 +-
 examples/2/example.mod | 2 +-
 examples/3/example.mod | 2 +-
 examples/4/example.mod | 2 +-
 examples/5/example.mod | 2 +-
 examples/6/example.mod | 2 +-
 examples/7/example.mod | 2 +-
 examples/8/example.mod | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/examples/1/example.mod b/examples/1/example.mod
index d3c136283..4f9151449 100644
--- a/examples/1/example.mod
+++ b/examples/1/example.mod
@@ -46,7 +46,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/2/example.mod b/examples/2/example.mod
index ae812a28d..9984b4d78 100644
--- a/examples/2/example.mod
+++ b/examples/2/example.mod
@@ -50,7 +50,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/3/example.mod b/examples/3/example.mod
index 21ef105b7..4cc913363 100644
--- a/examples/3/example.mod
+++ b/examples/3/example.mod
@@ -49,7 +49,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/4/example.mod b/examples/4/example.mod
index 87a2524ab..1d3e6ba54 100644
--- a/examples/4/example.mod
+++ b/examples/4/example.mod
@@ -63,7 +63,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/5/example.mod b/examples/5/example.mod
index 66917e0b3..623d0d0d3 100644
--- a/examples/5/example.mod
+++ b/examples/5/example.mod
@@ -65,7 +65,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/6/example.mod b/examples/6/example.mod
index dd207f50b..4178fef5b 100644
--- a/examples/6/example.mod
+++ b/examples/6/example.mod
@@ -64,7 +64,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero for non logged variables, and one for logged variables
 init = zeros(10, M_.endo_nbr+M_.exo_nbr);
diff --git a/examples/7/example.mod b/examples/7/example.mod
index c090a8140..d9d8f3578 100644
--- a/examples/7/example.mod
+++ b/examples/7/example.mod
@@ -64,7 +64,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
diff --git a/examples/8/example.mod b/examples/8/example.mod
index ce35414ba..237df34bd 100644
--- a/examples/8/example.mod
+++ b/examples/8/example.mod
@@ -72,7 +72,7 @@ end;
 get_companion_matrix('toto', 'pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
-pac.update.equation('pacman');
+pac.update.expectation('pacman');
 
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));

From d68698ffe9d5ea0e899967cb507ae6cd3d297ec2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 21 Jun 2018 18:53:57 +0200
Subject: [PATCH 32/56] Added example with estimation of the PAC equation by
 NLS.

---
 examples/9/clean       |   8 ++++
 examples/9/example.mod | 100 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 108 insertions(+)
 create mode 100755 examples/9/clean
 create mode 100644 examples/9/example.mod

diff --git a/examples/9/clean b/examples/9/clean
new file mode 100755
index 000000000..a0fd4a44a
--- /dev/null
+++ b/examples/9/clean
@@ -0,0 +1,8 @@
+#!/bin/sh
+
+rm -rf example
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
+rm -f ssr_zpac.m
diff --git a/examples/9/example.mod b/examples/9/example.mod
new file mode 100644
index 000000000..1febd6121
--- /dev/null
+++ b/examples/9/example.mod
@@ -0,0 +1,100 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
+
+//[pnames, enames, xnames, pid, eid, xid] = get_variables_and_parameters_in_equation('zpac', M_)
+
+// Define a structure describing the parameters to be estimated (with initial conditions). 
+eparams.e_c_m = .9;
+eparams.c_z_1 = .5;
+eparams.c_z_2 = .2;
+eparams.gamma = .1;
+
+// Define the dataset used for estimation
+edata = TrueData;
+edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
+
+pac.estimate('zpac', eparams, edata, 2005Q1:2120Q1);
+
+disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_2: %f', M_.params(strmatch('c_z_2', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of gamma: %f', M_.params(strmatch('gamma', M_.param_names, 'exact'))))

From 02a41ecbbe01bd888ff3ad9f33c28b824a6b00d3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Wed, 4 Jul 2018 10:07:24 +0200
Subject: [PATCH 33/56] Remove all generated m files.

---
 examples/9/clean | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/examples/9/clean b/examples/9/clean
index a0fd4a44a..68ebf1841 100755
--- a/examples/9/clean
+++ b/examples/9/clean
@@ -2,7 +2,6 @@
 
 rm -rf example
 rm  -f example*.json
-rm -f example*.m
 rm -f example*.mat
 rm -f example.log
-rm -f ssr_zpac.m
+rm -f *.m

From 908d5bc38611f99198f11378bc2d70905ffbdd23 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Wed, 11 Jul 2018 10:12:55 +0200
Subject: [PATCH 34/56] Added two examples.

---
 examples/10/clean       |  7 +++
 examples/10/example.mod | 96 +++++++++++++++++++++++++++++++++++++++++
 examples/11/clean       |  6 +++
 examples/11/example.mod | 57 ++++++++++++++++++++++++
 4 files changed, 166 insertions(+)
 create mode 100755 examples/10/clean
 create mode 100644 examples/10/example.mod
 create mode 100755 examples/11/clean
 create mode 100644 examples/11/example.mod

diff --git a/examples/10/clean b/examples/10/clean
new file mode 100755
index 000000000..68ebf1841
--- /dev/null
+++ b/examples/10/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm  -f example*.json
+rm -f example*.mat
+rm -f example.log
+rm -f *.m
diff --git a/examples/10/example.mod b/examples/10/example.mod
new file mode 100644
index 000000000..0212b1b0d
--- /dev/null
+++ b/examples/10/example.mod
@@ -0,0 +1,96 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
+
+//[pnames, enames, xnames, pid, eid, xid] = get_variables_and_parameters_in_equation('zpac', M_)
+
+// Define a structure describing the parameters to be estimated (with initial conditions). 
+eparams.e_c_m = .9;
+eparams.c_z_1 = .5;
+eparams.c_z_2 = .2;
+
+// Define the dataset used for estimation
+edata = TrueData;
+edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
+
+pac.estimate('zpac', eparams, edata, 2005Q1:2120Q1);
+
+disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_2: %f', M_.params(strmatch('c_z_2', M_.param_names, 'exact'))))
diff --git a/examples/11/clean b/examples/11/clean
new file mode 100755
index 000000000..be0d5e00c
--- /dev/null
+++ b/examples/11/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm -rf +example
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/examples/11/example.mod b/examples/11/example.mod
new file mode 100644
index 000000000..31c1512a2
--- /dev/null
+++ b/examples/11/example.mod
@@ -0,0 +1,57 @@
+// --+ options: json=compute, stochastic +--
+
+var y x z;
+
+varexo ex ey ez;
+
+parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 ; // VAR parameters
+
+parameters g beta e_c_m c_z_1 c_z_2;               // PAC equation parameters
+
+a_y_1 =  .2;
+a_y_2 =  .3;
+b_y_1 =  .1;
+b_y_2 =  .4;
+b_x_1 = -.1;
+b_x_2 = -.2;
+
+beta  =  .9;
+e_c_m =  .1;
+c_z_1 =  .7;
+c_z_2 = -.3;
+
+g = .1;
+
+var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, growth=g);
+
+model;
+
+[name='eq:y']
+y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+[name='eq:x', data_type='nonstationary']
+diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2)  + ex ;
+
+[name='eq:pac']
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex = 1.0;
+    var ey = 1.0;
+    var ez = 1.0;
+end;
+
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
\ No newline at end of file

From f4bbb227e7cc6bb6f40dcd5fafa8beab5d39db25 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Wed, 11 Jul 2018 10:13:29 +0200
Subject: [PATCH 35/56] Updated cleanup shell scripts.

---
 examples/1/clean | 3 +--
 examples/2/clean | 3 +--
 examples/3/clean | 3 +--
 examples/4/clean | 3 +--
 examples/5/clean | 3 +--
 examples/6/clean | 3 +--
 examples/7/clean | 3 +--
 examples/8/clean | 3 +--
 examples/9/clean | 5 ++---
 9 files changed, 10 insertions(+), 19 deletions(-)

diff --git a/examples/1/clean b/examples/1/clean
index 19ca1948b..be0d5e00c 100755
--- a/examples/1/clean
+++ b/examples/1/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/2/clean b/examples/2/clean
index 19ca1948b..be0d5e00c 100755
--- a/examples/2/clean
+++ b/examples/2/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/3/clean b/examples/3/clean
index 19ca1948b..be0d5e00c 100755
--- a/examples/3/clean
+++ b/examples/3/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/4/clean b/examples/4/clean
index 19ca1948b..be0d5e00c 100755
--- a/examples/4/clean
+++ b/examples/4/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/5/clean b/examples/5/clean
index 19ca1948b..be0d5e00c 100755
--- a/examples/5/clean
+++ b/examples/5/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/6/clean b/examples/6/clean
index 19ca1948b..2935a38ad 100755
--- a/examples/6/clean
+++ b/examples/6/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm  -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/7/clean b/examples/7/clean
index 19ca1948b..2935a38ad 100755
--- a/examples/7/clean
+++ b/examples/7/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm  -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/8/clean b/examples/8/clean
index 19ca1948b..2935a38ad 100755
--- a/examples/8/clean
+++ b/examples/8/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.m
+rm  -rf +example
 rm -f example*.mat
 rm -f example.log
\ No newline at end of file
diff --git a/examples/9/clean b/examples/9/clean
index 68ebf1841..a649d3c4f 100755
--- a/examples/9/clean
+++ b/examples/9/clean
@@ -1,7 +1,6 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
-rm -f example*.mat
+rm  -rf +example
 rm -f example.log
-rm -f *.m
+rm -f *.mat

From 64de92d93e52d5c5a302540c990b9e5cd7bc9902 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 16 Jul 2018 16:33:07 +0200
Subject: [PATCH 36/56] Changed name of the estimation routine for PAC
 equation.

---
 examples/10/example.mod | 2 +-
 examples/9/example.mod  | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/10/example.mod b/examples/10/example.mod
index 0212b1b0d..1d33a82ac 100644
--- a/examples/10/example.mod
+++ b/examples/10/example.mod
@@ -89,7 +89,7 @@ eparams.c_z_2 = .2;
 edata = TrueData;
 edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
 
-pac.estimate('zpac', eparams, edata, 2005Q1:2120Q1);
+pac.estimate.nls('zpac', eparams, edata, 2005Q1:2120Q1);
 
 disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
 disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
diff --git a/examples/9/example.mod b/examples/9/example.mod
index 1febd6121..908ae15a5 100644
--- a/examples/9/example.mod
+++ b/examples/9/example.mod
@@ -92,7 +92,7 @@ eparams.gamma = .1;
 edata = TrueData;
 edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
 
-pac.estimate('zpac', eparams, edata, 2005Q1:2120Q1);
+pac.estimate.nls('zpac', eparams, edata, 2005Q1:2120Q1);
 
 disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
 disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))

From 82ecdb5e91a0759a14cf8f4f837fd3e064c5845c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 16 Jul 2018 16:35:20 +0200
Subject: [PATCH 37/56] Fixed cleanup shell script.

---
 examples/9/clean | 1 +
 1 file changed, 1 insertion(+)

diff --git a/examples/9/clean b/examples/9/clean
index a649d3c4f..0d64aefde 100755
--- a/examples/9/clean
+++ b/examples/9/clean
@@ -4,3 +4,4 @@ rm -rf example
 rm  -rf +example
 rm -f example.log
 rm -f *.mat
+rm *.m

From efedc20d06c4043e3a40b827bcc8702e3e6301c8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 23 Jul 2018 15:30:48 +0200
Subject: [PATCH 38/56] Added montecarlo for comparing NLS and Iterative OLS
 estimation of PAC equation.

---
 examples/12-mc-iterative-ols/clean       |   6 ++
 examples/12-mc-iterative-ols/example.mod | 104 +++++++++++++++++++++++
 examples/12-mc-nls/clean                 |   7 ++
 examples/12-mc-nls/example.mod           | 100 ++++++++++++++++++++++
 4 files changed, 217 insertions(+)
 create mode 100755 examples/12-mc-iterative-ols/clean
 create mode 100644 examples/12-mc-iterative-ols/example.mod
 create mode 100755 examples/12-mc-nls/clean
 create mode 100644 examples/12-mc-nls/example.mod

diff --git a/examples/12-mc-iterative-ols/clean b/examples/12-mc-iterative-ols/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/examples/12-mc-iterative-ols/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/examples/12-mc-iterative-ols/example.mod b/examples/12-mc-iterative-ols/example.mod
new file mode 100644
index 000000000..32e059770
--- /dev/null
+++ b/examples/12-mc-iterative-ols/example.mod
@@ -0,0 +1,104 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta g;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+g=.1;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, growth=g, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+B = 20000;
+X = zeros(3,B);
+
+set_dynare_seed('default');
+options_.bnlms.set_dynare_seed_to_default = false;
+
+for i=1:B
+    e_c_m =  .5;
+    c_z_1 =  .2;
+    c_z_2 = -.1;
+    // Simulate the model for 500 periods
+    TrueData = simul_backward_model(initialconditions, 300);
+    // Define a structure describing the parameters to be estimated (with initial conditions). 
+    eparams.e_c_m = rand();
+    eparams.c_z_1 = .5*randn();
+    eparams.c_z_2 = .5*randn();
+    // Define the dataset used for estimation
+    edata = TrueData;
+    edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
+    pac.estimate.iterative_ols('zpac', eparams, edata, 2005Q1:2000Q1+200);
+    X(1,i) = M_.params(strmatch('e_c_m', M_.param_names, 'exact'));
+    X(2,i) = M_.params(strmatch('c_z_1', M_.param_names, 'exact'));
+    X(3,i) = M_.params(strmatch('c_z_2', M_.param_names, 'exact'));
+end
+
+mean(X, 2)
\ No newline at end of file
diff --git a/examples/12-mc-nls/clean b/examples/12-mc-nls/clean
new file mode 100755
index 000000000..0d64aefde
--- /dev/null
+++ b/examples/12-mc-nls/clean
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
+rm *.m
diff --git a/examples/12-mc-nls/example.mod b/examples/12-mc-nls/example.mod
new file mode 100644
index 000000000..7146a8e70
--- /dev/null
+++ b/examples/12-mc-nls/example.mod
@@ -0,0 +1,100 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+
+B = 20000;
+X = zeros(3,B);
+set_dynare_seed('default');
+
+options_.bnlms.set_dynare_seed_to_default = false;
+
+for i=1:B
+    // Simulate the model for 500 periods
+    TrueData = simul_backward_model(initialconditions, 300);
+    // Define a structure describing the parameters to be estimated (with initial conditions). 
+    eparams.e_c_m = rand();
+    eparams.c_z_1 = .5*randn();
+    eparams.c_z_2 = .5*randn();
+    // Define the dataset used for estimation
+    edata = TrueData;
+    edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
+    pac.estimate.nls('zpac', eparams, edata, 2005Q1:2000Q1+200);
+    X(1,i) = M_.params(strmatch('e_c_m', M_.param_names, 'exact'));
+    X(2,i) = M_.params(strmatch('c_z_1', M_.param_names, 'exact'));
+    X(3,i) = M_.params(strmatch('c_z_2', M_.param_names, 'exact'));
+end
+
+mean(X, 2)
\ No newline at end of file

From 4499388d316e62e1ac4c93515576a8f63813ff47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 23 Jul 2018 17:58:24 +0200
Subject: [PATCH 39/56] Changed initial conditions in Monte Carlo.

---
 examples/12-mc-iterative-ols/example.mod | 6 +++---
 examples/12-mc-nls/example.mod           | 6 +++---
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/examples/12-mc-iterative-ols/example.mod b/examples/12-mc-iterative-ols/example.mod
index 32e059770..a0c7a2894 100644
--- a/examples/12-mc-iterative-ols/example.mod
+++ b/examples/12-mc-iterative-ols/example.mod
@@ -89,9 +89,9 @@ for i=1:B
     // Simulate the model for 500 periods
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
-    eparams.e_c_m = rand();
-    eparams.c_z_1 = .5*randn();
-    eparams.c_z_2 = .5*randn();
+    eparams.e_c_m = .5;
+    eparams.c_z_1 = .2;
+    eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
     edata = TrueData;
     edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
diff --git a/examples/12-mc-nls/example.mod b/examples/12-mc-nls/example.mod
index 7146a8e70..70693b9be 100644
--- a/examples/12-mc-nls/example.mod
+++ b/examples/12-mc-nls/example.mod
@@ -85,9 +85,9 @@ for i=1:B
     // Simulate the model for 500 periods
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
-    eparams.e_c_m = rand();
-    eparams.c_z_1 = .5*randn();
-    eparams.c_z_2 = .5*randn();
+    eparams.e_c_m = .5;
+    eparams.c_z_1 = .2;
+    eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
     edata = TrueData;
     edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');

From c2a43f874c962e34e4b846a5a41de2809e139537 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 23 Jul 2018 18:00:11 +0200
Subject: [PATCH 40/56] Added new example.

---
 examples/13/clean       |  6 +++
 examples/13/example.mod | 92 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 98 insertions(+)
 create mode 100755 examples/13/clean
 create mode 100644 examples/13/example.mod

diff --git a/examples/13/clean b/examples/13/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/examples/13/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/examples/13/example.mod b/examples/13/example.mod
new file mode 100644
index 000000000..4b9f4f1cc
--- /dev/null
+++ b/examples/13/example.mod
@@ -0,0 +1,92 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 300);
+
+// Define a structure describing the parameters to be estimated (with initial conditions). 
+eparams.e_c_m = .9;
+eparams.c_z_1 = .5;
+eparams.c_z_2 = .2;
+
+// Define the dataset used for estimation
+edata = TrueData;
+edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
+pac.estimate.iterative_ols('zpac', eparams, edata, 2005Q1:2000Q1+200);
+
+disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_2: %f', M_.params(strmatch('c_z_2', M_.param_names, 'exact'))))

From 34186d64474898d10d2cf09beeb4bc238c1f85c7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 16 Aug 2018 10:11:56 +0200
Subject: [PATCH 41/56] Fixed cleanup script.

---
 examples/10/clean | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/10/clean b/examples/10/clean
index 68ebf1841..6f2442c33 100755
--- a/examples/10/clean
+++ b/examples/10/clean
@@ -1,7 +1,7 @@
 #!/bin/sh
 
 rm -rf example
-rm  -f example*.json
+rm -rf +example
 rm -f example*.mat
 rm -f example.log
-rm -f *.m
+rm -f *.m
\ No newline at end of file

From d63611bd5f371d133733afe667a14896a956a984 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Fri, 17 Aug 2018 21:32:41 +0200
Subject: [PATCH 42/56] Changed paths.

---
 {examples/1 => trend-component-1}/clean                           | 0
 {examples/4 => trend-component-1}/example.mod                     | 0
 {examples/12-mc-iterative-ols => trend-component-10}/clean        | 0
 {examples/13 => trend-component-10}/example.mod                   | 0
 {examples/11 => trend-component-2}/clean                          | 0
 {examples/5 => trend-component-2}/example.mod                     | 0
 {examples/6 => trend-component-3}/clean                           | 0
 {examples/6 => trend-component-3}/example.mod                     | 0
 {examples/7 => trend-component-4}/clean                           | 0
 {examples/7 => trend-component-4}/example.mod                     | 0
 {examples/8 => trend-component-5}/clean                           | 0
 {examples/8 => trend-component-5}/example.mod                     | 0
 {examples/12-mc-nls => trend-component-6}/clean                   | 0
 {examples/9 => trend-component-6}/example.mod                     | 0
 {examples/10 => trend-component-7}/clean                          | 0
 {examples/10 => trend-component-7}/example.mod                    | 0
 {examples/2 => trend-component-8}/clean                           | 0
 {examples/11 => trend-component-8}/example.mod                    | 0
 {examples/13 => trend-component-9-mc-iterative-ols}/clean         | 0
 .../example.mod                                                   | 0
 {examples/9 => trend-component-9-mc-nls}/clean                    | 0
 {examples/12-mc-nls => trend-component-9-mc-nls}/example.mod      | 0
 {examples/var => var-0}/clean                                     | 0
 {examples/var => var-0}/m1.mod                                    | 0
 {examples/var => var-0}/m2.mod                                    | 0
 {examples/var => var-0}/m3.mod                                    | 0
 {examples/var => var-0}/m4.mod                                    | 0
 {examples/3 => var-1}/clean                                       | 0
 {examples/1 => var-1}/example.mod                                 | 0
 {examples/4 => var-2}/clean                                       | 0
 {examples/2 => var-2}/example.mod                                 | 0
 {examples/5 => var-3}/clean                                       | 0
 {examples/3 => var-3}/example.mod                                 | 0
 33 files changed, 0 insertions(+), 0 deletions(-)
 rename {examples/1 => trend-component-1}/clean (100%)
 rename {examples/4 => trend-component-1}/example.mod (100%)
 rename {examples/12-mc-iterative-ols => trend-component-10}/clean (100%)
 rename {examples/13 => trend-component-10}/example.mod (100%)
 rename {examples/11 => trend-component-2}/clean (100%)
 rename {examples/5 => trend-component-2}/example.mod (100%)
 rename {examples/6 => trend-component-3}/clean (100%)
 rename {examples/6 => trend-component-3}/example.mod (100%)
 rename {examples/7 => trend-component-4}/clean (100%)
 rename {examples/7 => trend-component-4}/example.mod (100%)
 rename {examples/8 => trend-component-5}/clean (100%)
 rename {examples/8 => trend-component-5}/example.mod (100%)
 rename {examples/12-mc-nls => trend-component-6}/clean (100%)
 rename {examples/9 => trend-component-6}/example.mod (100%)
 rename {examples/10 => trend-component-7}/clean (100%)
 rename {examples/10 => trend-component-7}/example.mod (100%)
 rename {examples/2 => trend-component-8}/clean (100%)
 rename {examples/11 => trend-component-8}/example.mod (100%)
 rename {examples/13 => trend-component-9-mc-iterative-ols}/clean (100%)
 rename {examples/12-mc-iterative-ols => trend-component-9-mc-iterative-ols}/example.mod (100%)
 rename {examples/9 => trend-component-9-mc-nls}/clean (100%)
 rename {examples/12-mc-nls => trend-component-9-mc-nls}/example.mod (100%)
 rename {examples/var => var-0}/clean (100%)
 rename {examples/var => var-0}/m1.mod (100%)
 rename {examples/var => var-0}/m2.mod (100%)
 rename {examples/var => var-0}/m3.mod (100%)
 rename {examples/var => var-0}/m4.mod (100%)
 rename {examples/3 => var-1}/clean (100%)
 rename {examples/1 => var-1}/example.mod (100%)
 rename {examples/4 => var-2}/clean (100%)
 rename {examples/2 => var-2}/example.mod (100%)
 rename {examples/5 => var-3}/clean (100%)
 rename {examples/3 => var-3}/example.mod (100%)

diff --git a/examples/1/clean b/trend-component-1/clean
similarity index 100%
rename from examples/1/clean
rename to trend-component-1/clean
diff --git a/examples/4/example.mod b/trend-component-1/example.mod
similarity index 100%
rename from examples/4/example.mod
rename to trend-component-1/example.mod
diff --git a/examples/12-mc-iterative-ols/clean b/trend-component-10/clean
similarity index 100%
rename from examples/12-mc-iterative-ols/clean
rename to trend-component-10/clean
diff --git a/examples/13/example.mod b/trend-component-10/example.mod
similarity index 100%
rename from examples/13/example.mod
rename to trend-component-10/example.mod
diff --git a/examples/11/clean b/trend-component-2/clean
similarity index 100%
rename from examples/11/clean
rename to trend-component-2/clean
diff --git a/examples/5/example.mod b/trend-component-2/example.mod
similarity index 100%
rename from examples/5/example.mod
rename to trend-component-2/example.mod
diff --git a/examples/6/clean b/trend-component-3/clean
similarity index 100%
rename from examples/6/clean
rename to trend-component-3/clean
diff --git a/examples/6/example.mod b/trend-component-3/example.mod
similarity index 100%
rename from examples/6/example.mod
rename to trend-component-3/example.mod
diff --git a/examples/7/clean b/trend-component-4/clean
similarity index 100%
rename from examples/7/clean
rename to trend-component-4/clean
diff --git a/examples/7/example.mod b/trend-component-4/example.mod
similarity index 100%
rename from examples/7/example.mod
rename to trend-component-4/example.mod
diff --git a/examples/8/clean b/trend-component-5/clean
similarity index 100%
rename from examples/8/clean
rename to trend-component-5/clean
diff --git a/examples/8/example.mod b/trend-component-5/example.mod
similarity index 100%
rename from examples/8/example.mod
rename to trend-component-5/example.mod
diff --git a/examples/12-mc-nls/clean b/trend-component-6/clean
similarity index 100%
rename from examples/12-mc-nls/clean
rename to trend-component-6/clean
diff --git a/examples/9/example.mod b/trend-component-6/example.mod
similarity index 100%
rename from examples/9/example.mod
rename to trend-component-6/example.mod
diff --git a/examples/10/clean b/trend-component-7/clean
similarity index 100%
rename from examples/10/clean
rename to trend-component-7/clean
diff --git a/examples/10/example.mod b/trend-component-7/example.mod
similarity index 100%
rename from examples/10/example.mod
rename to trend-component-7/example.mod
diff --git a/examples/2/clean b/trend-component-8/clean
similarity index 100%
rename from examples/2/clean
rename to trend-component-8/clean
diff --git a/examples/11/example.mod b/trend-component-8/example.mod
similarity index 100%
rename from examples/11/example.mod
rename to trend-component-8/example.mod
diff --git a/examples/13/clean b/trend-component-9-mc-iterative-ols/clean
similarity index 100%
rename from examples/13/clean
rename to trend-component-9-mc-iterative-ols/clean
diff --git a/examples/12-mc-iterative-ols/example.mod b/trend-component-9-mc-iterative-ols/example.mod
similarity index 100%
rename from examples/12-mc-iterative-ols/example.mod
rename to trend-component-9-mc-iterative-ols/example.mod
diff --git a/examples/9/clean b/trend-component-9-mc-nls/clean
similarity index 100%
rename from examples/9/clean
rename to trend-component-9-mc-nls/clean
diff --git a/examples/12-mc-nls/example.mod b/trend-component-9-mc-nls/example.mod
similarity index 100%
rename from examples/12-mc-nls/example.mod
rename to trend-component-9-mc-nls/example.mod
diff --git a/examples/var/clean b/var-0/clean
similarity index 100%
rename from examples/var/clean
rename to var-0/clean
diff --git a/examples/var/m1.mod b/var-0/m1.mod
similarity index 100%
rename from examples/var/m1.mod
rename to var-0/m1.mod
diff --git a/examples/var/m2.mod b/var-0/m2.mod
similarity index 100%
rename from examples/var/m2.mod
rename to var-0/m2.mod
diff --git a/examples/var/m3.mod b/var-0/m3.mod
similarity index 100%
rename from examples/var/m3.mod
rename to var-0/m3.mod
diff --git a/examples/var/m4.mod b/var-0/m4.mod
similarity index 100%
rename from examples/var/m4.mod
rename to var-0/m4.mod
diff --git a/examples/3/clean b/var-1/clean
similarity index 100%
rename from examples/3/clean
rename to var-1/clean
diff --git a/examples/1/example.mod b/var-1/example.mod
similarity index 100%
rename from examples/1/example.mod
rename to var-1/example.mod
diff --git a/examples/4/clean b/var-2/clean
similarity index 100%
rename from examples/4/clean
rename to var-2/clean
diff --git a/examples/2/example.mod b/var-2/example.mod
similarity index 100%
rename from examples/2/example.mod
rename to var-2/example.mod
diff --git a/examples/5/clean b/var-3/clean
similarity index 100%
rename from examples/5/clean
rename to var-3/clean
diff --git a/examples/3/example.mod b/var-3/example.mod
similarity index 100%
rename from examples/3/example.mod
rename to var-3/example.mod

From fd4ca04ecbf4beeaa19ce559963a6af580e85dc4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Fri, 17 Aug 2018 22:28:06 +0200
Subject: [PATCH 43/56] Updated mod files with new interface
 ({trend_component,var}_model).

---
 trend-component-1/example.mod                                 | 4 ++--
 trend-component-2/example.mod                                 | 4 ++--
 trend-component-3/example.mod                                 | 4 ++--
 trend-component-4/example.mod                                 | 4 ++--
 trend-component-5/example.mod                                 | 4 ++--
 trend-component-6/example.mod                                 | 4 ++--
 trend-component-7/example.mod                                 | 4 ++--
 .../clean                                                     | 0
 .../example.mod                                               | 4 ++--
 {trend-component-9-mc-nls => trend-component-8-mc-nls}/clean  | 0
 .../example.mod                                               | 4 ++--
 .../clean                                                     | 0
 {trend-component-10 => trend-component-9}/example.mod         | 4 ++--
 var-1/example.mod                                             | 2 +-
 var-2/example.mod                                             | 2 +-
 var-3/example.mod                                             | 2 +-
 {trend-component-8 => var-4}/clean                            | 0
 {trend-component-8 => var-4}/example.mod                      | 2 +-
 18 files changed, 24 insertions(+), 24 deletions(-)
 rename {trend-component-10 => trend-component-8-mc-iterative-ols}/clean (100%)
 rename {trend-component-9-mc-iterative-ols => trend-component-8-mc-iterative-ols}/example.mod (92%)
 rename {trend-component-9-mc-nls => trend-component-8-mc-nls}/clean (100%)
 rename {trend-component-9-mc-nls => trend-component-8-mc-nls}/example.mod (92%)
 rename {trend-component-9-mc-iterative-ols => trend-component-9}/clean (100%)
 rename {trend-component-10 => trend-component-9}/example.mod (92%)
 rename {trend-component-8 => var-4}/clean (100%)
 rename {trend-component-8 => var-4}/example.mod (89%)

diff --git a/trend-component-1/example.mod b/trend-component-1/example.mod
index 1d3e6ba54..3afa7ed07 100644
--- a/trend-component-1/example.mod
+++ b/trend-component-1/example.mod
@@ -28,9 +28,9 @@ c_z_2 = -.1;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=[  'eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-2/example.mod b/trend-component-2/example.mod
index 623d0d0d3..92383c177 100644
--- a/trend-component-2/example.mod
+++ b/trend-component-2/example.mod
@@ -28,9 +28,9 @@ c_z_2 = -.3;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar'], trends=['eq:x1bar',  'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-3/example.mod b/trend-component-3/example.mod
index 4178fef5b..5ebcb93b0 100644
--- a/trend-component-3/example.mod
+++ b/trend-component-3/example.mod
@@ -28,9 +28,9 @@ c_z_2 = -.3;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar'], trends=['eq:x1bar',  'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-4/example.mod b/trend-component-4/example.mod
index d9d8f3578..0a58ce047 100644
--- a/trend-component-4/example.mod
+++ b/trend-component-4/example.mod
@@ -29,9 +29,9 @@ c_z_2 = -.1;
 
 gamma =  .9;
 
-var_model(model_name=toto, eqtags=[  'eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-5/example.mod b/trend-component-5/example.mod
index 237df34bd..05353fc2e 100644
--- a/trend-component-5/example.mod
+++ b/trend-component-5/example.mod
@@ -33,9 +33,9 @@ c_z_2 = -.1;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-6/example.mod b/trend-component-6/example.mod
index 908ae15a5..48b6f8f30 100644
--- a/trend-component-6/example.mod
+++ b/trend-component-6/example.mod
@@ -33,9 +33,9 @@ c_z_2 = -.1;
 
 gamma =  .7;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-7/example.mod b/trend-component-7/example.mod
index 1d33a82ac..cc1a6bf9e 100644
--- a/trend-component-7/example.mod
+++ b/trend-component-7/example.mod
@@ -31,9 +31,9 @@ e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-10/clean b/trend-component-8-mc-iterative-ols/clean
similarity index 100%
rename from trend-component-10/clean
rename to trend-component-8-mc-iterative-ols/clean
diff --git a/trend-component-9-mc-iterative-ols/example.mod b/trend-component-8-mc-iterative-ols/example.mod
similarity index 92%
rename from trend-component-9-mc-iterative-ols/example.mod
rename to trend-component-8-mc-iterative-ols/example.mod
index a0c7a2894..dedd34f8b 100644
--- a/trend-component-9-mc-iterative-ols/example.mod
+++ b/trend-component-8-mc-iterative-ols/example.mod
@@ -32,9 +32,9 @@ c_z_2 = -.1;
 
 g=.1;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, growth=g, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);
 
 model;
 
diff --git a/trend-component-9-mc-nls/clean b/trend-component-8-mc-nls/clean
similarity index 100%
rename from trend-component-9-mc-nls/clean
rename to trend-component-8-mc-nls/clean
diff --git a/trend-component-9-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
similarity index 92%
rename from trend-component-9-mc-nls/example.mod
rename to trend-component-8-mc-nls/example.mod
index 70693b9be..65acbff30 100644
--- a/trend-component-9-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -30,9 +30,9 @@ e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);
 
 model;
 
diff --git a/trend-component-9-mc-iterative-ols/clean b/trend-component-9/clean
similarity index 100%
rename from trend-component-9-mc-iterative-ols/clean
rename to trend-component-9/clean
diff --git a/trend-component-10/example.mod b/trend-component-9/example.mod
similarity index 92%
rename from trend-component-10/example.mod
rename to trend-component-9/example.mod
index 4b9f4f1cc..528c415af 100644
--- a/trend-component-10/example.mod
+++ b/trend-component-9/example.mod
@@ -30,9 +30,9 @@ e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
-var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/var-1/example.mod b/var-1/example.mod
index 4f9151449..9627f3473 100644
--- a/var-1/example.mod
+++ b/var-1/example.mod
@@ -22,7 +22,7 @@ c_z_2 = -.3;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman);
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/var-2/example.mod b/var-2/example.mod
index 9984b4d78..620fac421 100644
--- a/var-2/example.mod
+++ b/var-2/example.mod
@@ -24,7 +24,7 @@ gamma =  .7;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman);
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/var-3/example.mod b/var-3/example.mod
index 4cc913363..af1796a98 100644
--- a/var-3/example.mod
+++ b/var-3/example.mod
@@ -24,7 +24,7 @@ g = .02;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman);
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
 
 model;
 
diff --git a/trend-component-8/clean b/var-4/clean
similarity index 100%
rename from trend-component-8/clean
rename to var-4/clean
diff --git a/trend-component-8/example.mod b/var-4/example.mod
similarity index 89%
rename from trend-component-8/example.mod
rename to var-4/example.mod
index 31c1512a2..d1259effa 100644
--- a/trend-component-8/example.mod
+++ b/var-4/example.mod
@@ -24,7 +24,7 @@ g = .1;
 
 var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
 
-pac_model(var_model_name=toto, discount=beta, model_name=pacman, growth=g);
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman, growth=g);
 
 model;
 

From ecd6cd716fdaf4af58c86a9d591759ed35f3679b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Tue, 21 Aug 2018 22:17:58 +0200
Subject: [PATCH 44/56] Updated examples with new initialization routine for
 the PAC model.

---
 trend-component-1/example.mod                  | 4 ++--
 trend-component-2/example.mod                  | 4 ++--
 trend-component-3/example.mod                  | 4 ++--
 trend-component-4/example.mod                  | 4 ++--
 trend-component-5/example.mod                  | 4 ++--
 trend-component-6/example.mod                  | 4 ++--
 trend-component-7/example.mod                  | 4 ++--
 trend-component-8-mc-iterative-ols/example.mod | 5 +++--
 trend-component-8-mc-nls/example.mod           | 4 ++--
 trend-component-9/example.mod                  | 4 ++--
 var-1/example.mod                              | 3 ++-
 var-2/example.mod                              | 5 ++---
 var-3/example.mod                              | 4 ++--
 var-4/example.mod                              | 3 ++-
 14 files changed, 29 insertions(+), 27 deletions(-)

diff --git a/trend-component-1/example.mod b/trend-component-1/example.mod
index 3afa7ed07..dc4d84233 100644
--- a/trend-component-1/example.mod
+++ b/trend-component-1/example.mod
@@ -59,8 +59,8 @@ shocks;
     var ez = 1.0;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-2/example.mod b/trend-component-2/example.mod
index 92383c177..6f1dbdd89 100644
--- a/trend-component-2/example.mod
+++ b/trend-component-2/example.mod
@@ -61,8 +61,8 @@ shocks;
     var ez = 1.0;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-3/example.mod b/trend-component-3/example.mod
index 5ebcb93b0..f3a59a803 100644
--- a/trend-component-3/example.mod
+++ b/trend-component-3/example.mod
@@ -60,8 +60,8 @@ shocks;
     var ez = 1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-4/example.mod b/trend-component-4/example.mod
index 0a58ce047..ec435abf0 100644
--- a/trend-component-4/example.mod
+++ b/trend-component-4/example.mod
@@ -60,8 +60,8 @@ shocks;
     var ez = 1.0;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-5/example.mod b/trend-component-5/example.mod
index 05353fc2e..43eb56628 100644
--- a/trend-component-5/example.mod
+++ b/trend-component-5/example.mod
@@ -68,8 +68,8 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-6/example.mod b/trend-component-6/example.mod
index 48b6f8f30..6e390d358 100644
--- a/trend-component-6/example.mod
+++ b/trend-component-6/example.mod
@@ -68,8 +68,8 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-7/example.mod b/trend-component-7/example.mod
index cc1a6bf9e..1b7bc6831 100644
--- a/trend-component-7/example.mod
+++ b/trend-component-7/example.mod
@@ -66,8 +66,8 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-8-mc-iterative-ols/example.mod b/trend-component-8-mc-iterative-ols/example.mod
index dedd34f8b..1343f04ea 100644
--- a/trend-component-8-mc-iterative-ols/example.mod
+++ b/trend-component-8-mc-iterative-ols/example.mod
@@ -67,8 +67,9 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-8-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
index 65acbff30..44813fbf9 100644
--- a/trend-component-8-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -65,8 +65,8 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/trend-component-9/example.mod b/trend-component-9/example.mod
index 528c415af..aa80d6f7b 100644
--- a/trend-component-9/example.mod
+++ b/trend-component-9/example.mod
@@ -65,8 +65,8 @@ shocks;
     var ey = 0.1;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/var-1/example.mod b/var-1/example.mod
index 9627f3473..bb5d6e0ed 100644
--- a/var-1/example.mod
+++ b/var-1/example.mod
@@ -43,7 +43,8 @@ shocks;
     var ez = 1.0;
 end;
 
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/var-2/example.mod b/var-2/example.mod
index 620fac421..9f3e7068a 100644
--- a/var-2/example.mod
+++ b/var-2/example.mod
@@ -45,9 +45,8 @@ shocks;
     var ez = 1.0;
 end;
 
-
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/var-3/example.mod b/var-3/example.mod
index af1796a98..21a18a4c5 100644
--- a/var-3/example.mod
+++ b/var-3/example.mod
@@ -45,8 +45,8 @@ shocks;
     var ez = 1.0;
 end;
 
-// Build the companion matrix of the VAR model (toto).
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');
diff --git a/var-4/example.mod b/var-4/example.mod
index d1259effa..f5a8f62f0 100644
--- a/var-4/example.mod
+++ b/var-4/example.mod
@@ -45,7 +45,8 @@ shocks;
     var ez = 1.0;
 end;
 
-get_companion_matrix('toto', 'pacman');
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
 
 // Update the parameters of the PAC expectation model (h0 and h1 vectors).
 pac.update.expectation('pacman');

From 9e9025b677635d03b7f0a5e5dba82777f85e24d1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Tue, 21 Aug 2018 22:18:55 +0200
Subject: [PATCH 45/56] Clear structure containing the estimated PAC
 parameters.

---
 trend-component-6/example.mod                  | 1 +
 trend-component-7/example.mod                  | 1 +
 trend-component-8-mc-iterative-ols/example.mod | 1 +
 trend-component-8-mc-nls/example.mod           | 1 +
 trend-component-9/example.mod                  | 1 +
 5 files changed, 5 insertions(+)

diff --git a/trend-component-6/example.mod b/trend-component-6/example.mod
index 6e390d358..3e35606bc 100644
--- a/trend-component-6/example.mod
+++ b/trend-component-6/example.mod
@@ -83,6 +83,7 @@ TrueData = simul_backward_model(initialconditions, 500);
 //[pnames, enames, xnames, pid, eid, xid] = get_variables_and_parameters_in_equation('zpac', M_)
 
 // Define a structure describing the parameters to be estimated (with initial conditions). 
+clear eparams
 eparams.e_c_m = .9;
 eparams.c_z_1 = .5;
 eparams.c_z_2 = .2;
diff --git a/trend-component-7/example.mod b/trend-component-7/example.mod
index 1b7bc6831..100c87e7f 100644
--- a/trend-component-7/example.mod
+++ b/trend-component-7/example.mod
@@ -81,6 +81,7 @@ TrueData = simul_backward_model(initialconditions, 500);
 //[pnames, enames, xnames, pid, eid, xid] = get_variables_and_parameters_in_equation('zpac', M_)
 
 // Define a structure describing the parameters to be estimated (with initial conditions). 
+clear eparams
 eparams.e_c_m = .9;
 eparams.c_z_1 = .5;
 eparams.c_z_2 = .2;
diff --git a/trend-component-8-mc-iterative-ols/example.mod b/trend-component-8-mc-iterative-ols/example.mod
index 1343f04ea..af80fb534 100644
--- a/trend-component-8-mc-iterative-ols/example.mod
+++ b/trend-component-8-mc-iterative-ols/example.mod
@@ -90,6 +90,7 @@ for i=1:B
     // Simulate the model for 500 periods
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
+    clear eparams
     eparams.e_c_m = .5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
diff --git a/trend-component-8-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
index 44813fbf9..1ba97d038 100644
--- a/trend-component-8-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -85,6 +85,7 @@ for i=1:B
     // Simulate the model for 500 periods
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
+    clear eparams
     eparams.e_c_m = .5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
diff --git a/trend-component-9/example.mod b/trend-component-9/example.mod
index aa80d6f7b..2481278c9 100644
--- a/trend-component-9/example.mod
+++ b/trend-component-9/example.mod
@@ -78,6 +78,7 @@ initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M
 TrueData = simul_backward_model(initialconditions, 300);
 
 // Define a structure describing the parameters to be estimated (with initial conditions). 
+clear eparams
 eparams.e_c_m = .9;
 eparams.c_z_1 = .5;
 eparams.c_z_2 = .2;

From ad871c84932735a968604e61e45e6722b992c3ce Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Tue, 21 Aug 2018 22:19:59 +0200
Subject: [PATCH 46/56] Added routine to launch all the tests.

---
 run_all_tests.m | 63 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 run_all_tests.m

diff --git a/run_all_tests.m b/run_all_tests.m
new file mode 100644
index 000000000..b0d3442c8
--- /dev/null
+++ b/run_all_tests.m
@@ -0,0 +1,63 @@
+function run_all_tests()
+
+% Copyright (C) 2018 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
+
+r = [];
+
+r = [r; run_this_test('var-1')];
+r = [r; run_this_test('var-2')];
+r = [r; run_this_test('var-3')];
+r = [r; run_this_test('var-4')];
+
+r = [r; run_this_test('trend-component-1')];
+r = [r; run_this_test('trend-component-2')];
+r = [r; run_this_test('trend-component-3')];
+r = [r; run_this_test('trend-component-4')];
+r = [r; run_this_test('trend-component-5')];
+r = [r; run_this_test('trend-component-6')];
+r = [r; run_this_test('trend-component-7')];
+r = [r; run_this_test('trend-component-9')];
+
+print_results(r);
+
+function o = run_this_test(folder)
+try
+    cd(folder)
+    tstart = tic;
+    clear M_ oo_ options_
+    dynare example
+    elapsed = toc(tstart);
+    o = {folder, true, elapsed};
+    system('./clean')
+    cd ..
+catch
+    o = {folder, false, NaN};
+    system('./clean')
+    cd ..
+end
+
+function print_results(r)
+message = sprintf('Testsuite results (PAC model):\n');
+for i = 1:size(r, 1)
+    if r{i, 2}
+        message = sprintf('%s\n%s\t\t PASS (%ss)', message, r{i,1}, num2str(r{i,3}));
+    else
+        message = sprintf('%s\n%s\t\t FAILED', message, r{i,1});
+    end
+end
+disp(message)
\ No newline at end of file

From 03f75963b9e8776f81268c2ea94dc9b200c2c0f9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Mon, 27 Aug 2018 15:09:02 +0200
Subject: [PATCH 47/56] Added missing g (growth) parameter.

---
 trend-component-8-mc-nls/example.mod | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/trend-component-8-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
index 1ba97d038..d8ea91d07 100644
--- a/trend-component-8-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -8,7 +8,7 @@ parameters
        rho_1 rho_2
        a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
 	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
-	   e_c_m c_z_1 c_z_2 beta ;
+	   e_c_m c_z_1 c_z_2 beta g;
 
 rho_1 = .9;
 rho_2 = -.2;
@@ -30,6 +30,8 @@ e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
+g = .1;
+
 trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
 
 pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);

From eff4fee4838d4b9cbd75d1c27eca58fd64d49ded Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Tue, 28 Aug 2018 17:26:24 +0200
Subject: [PATCH 48/56] Added new test.

---
 run_all_tests.m                |  3 +-
 trend-component-10/clean       |  6 +++
 trend-component-10/example.mod | 96 ++++++++++++++++++++++++++++++++++
 3 files changed, 104 insertions(+), 1 deletion(-)
 create mode 100755 trend-component-10/clean
 create mode 100644 trend-component-10/example.mod

diff --git a/run_all_tests.m b/run_all_tests.m
index b0d3442c8..94b0f43de 100644
--- a/run_all_tests.m
+++ b/run_all_tests.m
@@ -32,6 +32,7 @@ r = [r; run_this_test('trend-component-5')];
 r = [r; run_this_test('trend-component-6')];
 r = [r; run_this_test('trend-component-7')];
 r = [r; run_this_test('trend-component-9')];
+r = [r; run_this_test('trend-component-10')];
 
 print_results(r);
 
@@ -60,4 +61,4 @@ for i = 1:size(r, 1)
         message = sprintf('%s\n%s\t\t FAILED', message, r{i,1});
     end
 end
-disp(message)
\ No newline at end of file
+disp(message)
diff --git a/trend-component-10/clean b/trend-component-10/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/trend-component-10/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/trend-component-10/example.mod b/trend-component-10/example.mod
new file mode 100644
index 000000000..38c832c8a
--- /dev/null
+++ b/trend-component-10/example.mod
@@ -0,0 +1,96 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
+
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(log(x1)) = a_x1_0*(log(x1(-1))-x1bar(-1)) + a_x1_1*diff(log(x1(-1))) + a_x1_2*diff(log(x1(-2))) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(log(x1(-1))) + a_x2_2*diff(log(x1(-2))) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(log(x1(-1))-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = .1;
+    var ex2bar = .1;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+INITIALCONDITIONS = zeros(10, M_.endo_nbr+M_.exo_nbr);
+INITIALCONDITIONS(:,1) = ones(10, 1);
+initialconditions = dseries(INITIALCONDITIONS, 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 300);
+
+// Define a structure describing the parameters to be estimated (with initial conditions). 
+clear eparams
+eparams.e_c_m = .9;
+eparams.c_z_1 = .5;
+
+eparams.c_z_2 = .2;
+
+// Define the dataset used for estimation
+edata = TrueData;
+edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
+pac.estimate.iterative_ols('zpac', eparams, edata, 2005Q1:2000Q1+200);
+
+disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_2: %f', M_.params(strmatch('c_z_2', M_.param_names, 'exact'))))

From 27f2f198e4d01c5adf4aa885fc182e88a954e155 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Tue, 28 Aug 2018 19:20:34 +0200
Subject: [PATCH 49/56] Fixed error correction term in PAC.

---
 trend-component-1/example.mod                  |  4 ++--
 trend-component-10/example.mod                 |  4 ++--
 trend-component-2/example.mod                  |  5 ++---
 trend-component-3/example.mod                  |  4 ++--
 trend-component-4/example.mod                  |  4 ++--
 trend-component-5/example.mod                  |  4 ++--
 trend-component-6/example.mod                  |  4 ++--
 trend-component-7/example.mod                  |  4 ++--
 trend-component-8-mc-iterative-ols/example.mod |  8 ++++----
 trend-component-8-mc-nls/example.mod           | 11 +++++------
 trend-component-9/example.mod                  |  6 +++---
 var-1/example.mod                              |  4 ++--
 var-2/example.mod                              |  4 ++--
 var-3/example.mod                              |  4 ++--
 var-4/example.mod                              |  4 ++--
 15 files changed, 36 insertions(+), 38 deletions(-)

diff --git a/trend-component-1/example.mod b/trend-component-1/example.mod
index dc4d84233..608c3b0cf 100644
--- a/trend-component-1/example.mod
+++ b/trend-component-1/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -47,7 +47,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/trend-component-10/example.mod b/trend-component-10/example.mod
index 38c832c8a..8450443ee 100644
--- a/trend-component-10/example.mod
+++ b/trend-component-10/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -52,7 +52,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(log(x1(-1))-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-log(x1(-1))) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/trend-component-2/example.mod b/trend-component-2/example.mod
index 6f1dbdd89..41ea6b4f5 100644
--- a/trend-component-2/example.mod
+++ b/trend-component-2/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .1;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .07;
 c_z_2 = -.3;
 
@@ -43,12 +43,11 @@ diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(diff(x1(-1))) + a_x2_2*diff(d
 [name='eq:x1bar', data_type='nonstationary']
 diff(x1bar) = diff(x1bar(-1)) + ex1bar;
 
-
 [name='eq:x2bar', data_type='nonstationary']
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*( e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 
 end;
diff --git a/trend-component-3/example.mod b/trend-component-3/example.mod
index f3a59a803..724224939 100644
--- a/trend-component-3/example.mod
+++ b/trend-component-3/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .1;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .07;
 c_z_2 = -.3;
 
@@ -47,7 +47,7 @@ diff(x1bar) = diff(x1bar(-1)) + ex1bar;
 log(x2bar) = log(x2bar(-1)) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 
 end;
diff --git a/trend-component-4/example.mod b/trend-component-4/example.mod
index ec435abf0..75b19c8bd 100644
--- a/trend-component-4/example.mod
+++ b/trend-component-4/example.mod
@@ -23,7 +23,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -48,7 +48,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/trend-component-5/example.mod b/trend-component-5/example.mod
index 43eb56628..3fad9a320 100644
--- a/trend-component-5/example.mod
+++ b/trend-component-5/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -55,7 +55,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
 
 end;
 
diff --git a/trend-component-6/example.mod b/trend-component-6/example.mod
index 3e35606bc..ee3ac75ca 100644
--- a/trend-component-6/example.mod
+++ b/trend-component-6/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -55,7 +55,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
 
 end;
 
diff --git a/trend-component-7/example.mod b/trend-component-7/example.mod
index 100c87e7f..a13cc4ecb 100644
--- a/trend-component-7/example.mod
+++ b/trend-component-7/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -53,7 +53,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/trend-component-8-mc-iterative-ols/example.mod b/trend-component-8-mc-iterative-ols/example.mod
index af80fb534..7128ac66b 100644
--- a/trend-component-8-mc-iterative-ols/example.mod
+++ b/trend-component-8-mc-iterative-ols/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -54,7 +54,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -77,7 +77,7 @@ pac.update.expectation('pacman');
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
 
-B = 20000;
+B = 1;
 X = zeros(3,B);
 
 set_dynare_seed('default');
@@ -91,7 +91,7 @@ for i=1:B
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
     clear eparams
-    eparams.e_c_m = .5;
+    eparams.e_c_m = -.5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
diff --git a/trend-component-8-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
index d8ea91d07..f06d6278a 100644
--- a/trend-component-8-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -54,7 +54,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -76,11 +76,10 @@ pac.update.expectation('pacman');
 // Set initial conditions to zero. Please use more sensible values if any...
 initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
 
-
-B = 20000;
+B = 1;
 X = zeros(3,B);
-set_dynare_seed('default');
 
+set_dynare_seed('default');
 options_.bnlms.set_dynare_seed_to_default = false;
 
 for i=1:B
@@ -88,7 +87,7 @@ for i=1:B
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
     clear eparams
-    eparams.e_c_m = .5;
+    eparas.e_c_m = -.5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
diff --git a/trend-component-9/example.mod b/trend-component-9/example.mod
index 2481278c9..51a5d223a 100644
--- a/trend-component-9/example.mod
+++ b/trend-component-9/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  .5;
+e_c_m =  -.5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -52,7 +52,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -79,7 +79,7 @@ TrueData = simul_backward_model(initialconditions, 300);
 
 // Define a structure describing the parameters to be estimated (with initial conditions). 
 clear eparams
-eparams.e_c_m = .9;
+eparams.e_c_m = -.9;
 eparams.c_z_1 = .5;
 eparams.c_z_2 = .2;
 
diff --git a/var-1/example.mod b/var-1/example.mod
index bb5d6e0ed..e60ca8749 100644
--- a/var-1/example.mod
+++ b/var-1/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -33,7 +33,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/var-2/example.mod b/var-2/example.mod
index 9f3e7068a..b13654a75 100644
--- a/var-2/example.mod
+++ b/var-2/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/var-3/example.mod b/var-3/example.mod
index 21a18a4c5..a9884607e 100644
--- a/var-3/example.mod
+++ b/var-3/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/var-4/example.mod b/var-4/example.mod
index f5a8f62f0..55ef24c4c 100644
--- a/var-4/example.mod
+++ b/var-4/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  .1;
+e_c_m =  -.1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2)  + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 

From 48c1370071c50033be3df4936a86c4ddb636872b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Wed, 29 Aug 2018 10:06:11 +0200
Subject: [PATCH 50/56] Added new test.

---
 run_all_tests.m                |  3 +-
 trend-component-11/clean       |  6 +++
 trend-component-11/example.mod | 74 ++++++++++++++++++++++++++++++++++
 3 files changed, 82 insertions(+), 1 deletion(-)
 create mode 100755 trend-component-11/clean
 create mode 100644 trend-component-11/example.mod

diff --git a/run_all_tests.m b/run_all_tests.m
index 94b0f43de..51f31cbc3 100644
--- a/run_all_tests.m
+++ b/run_all_tests.m
@@ -33,6 +33,7 @@ r = [r; run_this_test('trend-component-6')];
 r = [r; run_this_test('trend-component-7')];
 r = [r; run_this_test('trend-component-9')];
 r = [r; run_this_test('trend-component-10')];
+r = [r; run_this_test('trend-component-11')];
 
 print_results(r);
 
@@ -55,7 +56,7 @@ end
 function print_results(r)
 message = sprintf('Testsuite results (PAC model):\n');
 for i = 1:size(r, 1)
-    if r{i, 2}
+    if r{i,2}
         message = sprintf('%s\n%s\t\t PASS (%ss)', message, r{i,1}, num2str(r{i,3}));
     else
         message = sprintf('%s\n%s\t\t FAILED', message, r{i,1});
diff --git a/trend-component-11/clean b/trend-component-11/clean
new file mode 100755
index 000000000..2935a38ad
--- /dev/null
+++ b/trend-component-11/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example*.mat
+rm -f example.log
\ No newline at end of file
diff --git a/trend-component-11/example.mod b/trend-component-11/example.mod
new file mode 100644
index 000000000..63492d5bb
--- /dev/null
+++ b/trend-component-11/example.mod
@@ -0,0 +1,74 @@
+// --+ options: json=compute, transform_unary_ops, stochastic +--
+
+var x1 x2 x1bar x2bar z ;
+
+varexo ex1 ex2 ex1bar ex2bar ez ;
+
+parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+a_x1_0 =  -.9999;
+a_x1_1 =  .4;
+a_x1_2 =  0;//.3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = 0;//.2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  0;//-.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = 0;//.2;
+
+beta  =  .1;
+e_c_m =  -.1;
+c_z_1 =  .07;
+c_z_2 = -.3;
+
+gamma =  .7;
+
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar',  'eq:x2bar'], trends=['eq:x1bar',  'eq:x2bar']);
+
+pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
+
+model;
+
+[name='eq:x1', data_type='nonstationary']
+diff(diff(log(x1))) = a_x1_0*(diff(log(x1(-1)))-x1bar(-1)) + a_x1_1*diff(diff(log(x1(-1)))) + a_x1_2*diff(diff(x1(-2))) + a_x1_x2_1*diff(log(x2(-1))) + a_x1_x2_2*diff(log(x2(-2))) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(log(x2)) = a_x2_0*(log(x2(-1))-x2bar(-1)) + a_x2_1*diff(diff(log(x1(-1)))) + a_x2_2*diff(diff(log(x1(-2)))) + a_x2_x1_1*diff(log(x2(-1))) + a_x2_x1_2*diff(log(x2(-2))) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='eq:pac']
+diff(z) = gamma*(e_c_m*(z(-1)-log(x1(-1))) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+
+
+end;
+
+shocks;
+    var ex1 = 1;
+    var ex2 = 1;
+    var ex1bar = .1;
+    var ex2bar = .11;
+    var ez = 1;
+end;
+
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero for non logged variables, and one for logged variables
+init = .1*ones(10,M_.endo_nbr+M_.exo_nbr);
+initialconditions = dseries(init, 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 10);
\ No newline at end of file

From 2a991516bf0eeb6c4f604791fa5e8b7cfa37cbbd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemia=20=28Scylla=29?= <stepan@dynare.org>
Date: Wed, 29 Aug 2018 18:04:10 +0200
Subject: [PATCH 51/56] Added new example with time varying growth in PAC.

---
 trend-component-12/clean       |   6 ++
 trend-component-12/example.mod | 105 +++++++++++++++++++++++++++++++++
 2 files changed, 111 insertions(+)
 create mode 100755 trend-component-12/clean
 create mode 100644 trend-component-12/example.mod

diff --git a/trend-component-12/clean b/trend-component-12/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/trend-component-12/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/trend-component-12/example.mod b/trend-component-12/example.mod
new file mode 100644
index 000000000..42997b4cb
--- /dev/null
+++ b/trend-component-12/example.mod
@@ -0,0 +1,105 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey g;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  -.5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
+
+pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+    var g = 0.1;
+end;
+
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+B = 1;
+X = zeros(3,B);
+
+set_dynare_seed('default');
+options_.bnlms.set_dynare_seed_to_default = false;
+
+for i=1:B
+    e_c_m = -.5;
+    c_z_1 =  .2;
+    c_z_2 = -.1;
+    // Simulate the model for 500 periods
+    TrueData = simul_backward_model(initialconditions, 300);
+    // Define a structure describing the parameters to be estimated (with initial conditions). 
+    clear eparams
+    eparams.e_c_m = -.5;
+    eparams.c_z_1 = .2;
+    eparams.c_z_2 =-.1;
+    // Define the dataset used for estimation
+    edata = TrueData;
+    edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
+    pac.estimate.iterative_ols('zpac', eparams, edata, 2005Q1:2000Q1+200);
+    X(1,i) = M_.params(strmatch('e_c_m', M_.param_names, 'exact'));
+    X(2,i) = M_.params(strmatch('c_z_1', M_.param_names, 'exact'));
+    X(3,i) = M_.params(strmatch('c_z_2', M_.param_names, 'exact'));
+end
+
+mean(X, 2)
\ No newline at end of file

From 9414731bbab67b2c0e7d6610193188cbf9e97d66 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Mon, 3 Sep 2018 17:33:24 +0200
Subject: [PATCH 52/56] Activate twelveth test with trend_component auxiliary
 model.

---
 run_all_tests.m | 1 +
 1 file changed, 1 insertion(+)

diff --git a/run_all_tests.m b/run_all_tests.m
index 51f31cbc3..ae22d5de0 100644
--- a/run_all_tests.m
+++ b/run_all_tests.m
@@ -34,6 +34,7 @@ r = [r; run_this_test('trend-component-7')];
 r = [r; run_this_test('trend-component-9')];
 r = [r; run_this_test('trend-component-10')];
 r = [r; run_this_test('trend-component-11')];
+r = [r; run_this_test('trend-component-12')];
 
 print_results(r);
 

From 1a071915fa00537f2a44295c10177bcb0be935d2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 6 Sep 2018 18:02:45 +0200
Subject: [PATCH 53/56] Updated tests/examples with new ordering of error
 correction term.

---
 trend-component-1/example.mod                  |  4 ++--
 trend-component-10/example.mod                 |  5 ++---
 trend-component-11/example.mod                 |  4 ++--
 trend-component-12/example.mod                 |  8 ++++----
 trend-component-2/example.mod                  |  4 ++--
 trend-component-3/example.mod                  |  4 ++--
 trend-component-4/example.mod                  |  4 ++--
 trend-component-5/example.mod                  |  4 ++--
 trend-component-6/example.mod                  |  4 ++--
 trend-component-7/example.mod                  |  4 ++--
 trend-component-8-mc-iterative-ols/example.mod |  4 ++--
 trend-component-8-mc-nls/example.mod           |  6 +++---
 trend-component-9/example.mod                  | 10 +++++-----
 var-1/example.mod                              |  4 ++--
 var-2/example.mod                              |  4 ++--
 var-3/example.mod                              |  4 ++--
 var-4/example.mod                              |  4 ++--
 17 files changed, 40 insertions(+), 41 deletions(-)

diff --git a/trend-component-1/example.mod b/trend-component-1/example.mod
index 608c3b0cf..dc4d84233 100644
--- a/trend-component-1/example.mod
+++ b/trend-component-1/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -47,7 +47,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/trend-component-10/example.mod b/trend-component-10/example.mod
index 8450443ee..bf99be3b2 100644
--- a/trend-component-10/example.mod
+++ b/trend-component-10/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -52,7 +52,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-log(x1(-1))) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(log(x1(-1))-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -83,7 +83,6 @@ TrueData = simul_backward_model(initialconditions, 300);
 clear eparams
 eparams.e_c_m = .9;
 eparams.c_z_1 = .5;
-
 eparams.c_z_2 = .2;
 
 // Define the dataset used for estimation
diff --git a/trend-component-11/example.mod b/trend-component-11/example.mod
index 63492d5bb..09ebeb275 100644
--- a/trend-component-11/example.mod
+++ b/trend-component-11/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = 0;//.2;
 
 beta  =  .1;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .07;
 c_z_2 = -.3;
 
@@ -47,7 +47,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-log(x1(-1))) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(log(x1(-1))-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 
 end;
diff --git a/trend-component-12/example.mod b/trend-component-12/example.mod
index 42997b4cb..ef916581a 100644
--- a/trend-component-12/example.mod
+++ b/trend-component-12/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -52,7 +52,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -83,14 +83,14 @@ set_dynare_seed('default');
 options_.bnlms.set_dynare_seed_to_default = false;
 
 for i=1:B
-    e_c_m = -.5;
+    e_c_m =  .5;
     c_z_1 =  .2;
     c_z_2 = -.1;
     // Simulate the model for 500 periods
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
     clear eparams
-    eparams.e_c_m = -.5;
+    eparams.e_c_m = .5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
diff --git a/trend-component-2/example.mod b/trend-component-2/example.mod
index 41ea6b4f5..757f4b610 100644
--- a/trend-component-2/example.mod
+++ b/trend-component-2/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .1;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .07;
 c_z_2 = -.3;
 
@@ -47,7 +47,7 @@ diff(x1bar) = diff(x1bar(-1)) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*( e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*( e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 
 end;
diff --git a/trend-component-3/example.mod b/trend-component-3/example.mod
index 724224939..f3a59a803 100644
--- a/trend-component-3/example.mod
+++ b/trend-component-3/example.mod
@@ -22,7 +22,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .1;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .07;
 c_z_2 = -.3;
 
@@ -47,7 +47,7 @@ diff(x1bar) = diff(x1bar(-1)) + ex1bar;
 log(x2bar) = log(x2bar(-1)) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 
 end;
diff --git a/trend-component-4/example.mod b/trend-component-4/example.mod
index 75b19c8bd..ec435abf0 100644
--- a/trend-component-4/example.mod
+++ b/trend-component-4/example.mod
@@ -23,7 +23,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -48,7 +48,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/trend-component-5/example.mod b/trend-component-5/example.mod
index 3fad9a320..43eb56628 100644
--- a/trend-component-5/example.mod
+++ b/trend-component-5/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -55,7 +55,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
 
 end;
 
diff --git a/trend-component-6/example.mod b/trend-component-6/example.mod
index ee3ac75ca..3e35606bc 100644
--- a/trend-component-6/example.mod
+++ b/trend-component-6/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -55,7 +55,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = gamma*(e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
 
 end;
 
diff --git a/trend-component-7/example.mod b/trend-component-7/example.mod
index a13cc4ecb..100c87e7f 100644
--- a/trend-component-7/example.mod
+++ b/trend-component-7/example.mod
@@ -27,7 +27,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -53,7 +53,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/trend-component-8-mc-iterative-ols/example.mod b/trend-component-8-mc-iterative-ols/example.mod
index 7128ac66b..26438fcb3 100644
--- a/trend-component-8-mc-iterative-ols/example.mod
+++ b/trend-component-8-mc-iterative-ols/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -54,7 +54,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/trend-component-8-mc-nls/example.mod b/trend-component-8-mc-nls/example.mod
index f06d6278a..bf6549072 100644
--- a/trend-component-8-mc-nls/example.mod
+++ b/trend-component-8-mc-nls/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -54,7 +54,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -87,7 +87,7 @@ for i=1:B
     TrueData = simul_backward_model(initialconditions, 300);
     // Define a structure describing the parameters to be estimated (with initial conditions). 
     clear eparams
-    eparas.e_c_m = -.5;
+    eparas.e_c_m =  .5;
     eparams.c_z_1 = .2;
     eparams.c_z_2 =-.1;
     // Define the dataset used for estimation
diff --git a/trend-component-9/example.mod b/trend-component-9/example.mod
index 51a5d223a..455e86f6c 100644
--- a/trend-component-9/example.mod
+++ b/trend-component-9/example.mod
@@ -26,7 +26,7 @@ a_x2_x1_1 = -.1;
 a_x2_x1_2 = .2;
 
 beta  =  .2;
-e_c_m =  -.5;
+e_c_m =  .5;
 c_z_1 =  .2;
 c_z_2 = -.1;
 
@@ -52,7 +52,7 @@ x1bar = x1bar(-1) + ex1bar;
 x2bar = x2bar(-1) + ex2bar;
 
 [name='zpac']
-diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
@@ -79,9 +79,9 @@ TrueData = simul_backward_model(initialconditions, 300);
 
 // Define a structure describing the parameters to be estimated (with initial conditions). 
 clear eparams
-eparams.e_c_m = -.9;
-eparams.c_z_1 = .5;
-eparams.c_z_2 = .2;
+eparams.e_c_m =  .9;
+eparams.c_z_1 =  .5;
+eparams.c_z_2 =  .2;
 
 // Define the dataset used for estimation
 edata = TrueData;
diff --git a/var-1/example.mod b/var-1/example.mod
index e60ca8749..bb5d6e0ed 100644
--- a/var-1/example.mod
+++ b/var-1/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -33,7 +33,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/var-2/example.mod b/var-2/example.mod
index b13654a75..9f3e7068a 100644
--- a/var-2/example.mod
+++ b/var-2/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = gamma*(e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
+diff(z) = gamma*(e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
 
 end;
 
diff --git a/var-3/example.mod b/var-3/example.mod
index a9884607e..21a18a4c5 100644
--- a/var-3/example.mod
+++ b/var-3/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 
diff --git a/var-4/example.mod b/var-4/example.mod
index 55ef24c4c..f5a8f62f0 100644
--- a/var-4/example.mod
+++ b/var-4/example.mod
@@ -16,7 +16,7 @@ b_x_1 = -.1;
 b_x_2 = -.2;
 
 beta  =  .9;
-e_c_m =  -.1;
+e_c_m =  .1;
 c_z_1 =  .7;
 c_z_2 = -.3;
 
@@ -35,7 +35,7 @@ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
 diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2)  + ex ;
 
 [name='eq:pac']
-diff(z) = e_c_m*(z(-1)-x(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
 
 end;
 

From ea768b9ff9f4703c4d36184ece96a42b843a6a85 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 6 Sep 2018 18:03:19 +0200
Subject: [PATCH 54/56] Added new tests.

---
 run_all_tests.m                 |  2 +
 trend-component-13a/clean       |  6 +++
 trend-component-13a/example.mod | 74 +++++++++++++++++++++++++++++++++
 trend-component-13b/clean       |  6 +++
 trend-component-13b/example.mod | 74 +++++++++++++++++++++++++++++++++
 5 files changed, 162 insertions(+)
 create mode 100755 trend-component-13a/clean
 create mode 100644 trend-component-13a/example.mod
 create mode 100755 trend-component-13b/clean
 create mode 100644 trend-component-13b/example.mod

diff --git a/run_all_tests.m b/run_all_tests.m
index ae22d5de0..27cf54e49 100644
--- a/run_all_tests.m
+++ b/run_all_tests.m
@@ -35,6 +35,8 @@ r = [r; run_this_test('trend-component-9')];
 r = [r; run_this_test('trend-component-10')];
 r = [r; run_this_test('trend-component-11')];
 r = [r; run_this_test('trend-component-12')];
+r = [r; run_this_test('trend-component-13a')];
+r = [r; run_this_test('trend-component-13b')];
 
 print_results(r);
 
diff --git a/trend-component-13a/clean b/trend-component-13a/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/trend-component-13a/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/trend-component-13a/example.mod b/trend-component-13a/example.mod
new file mode 100644
index 000000000..f7355a201
--- /dev/null
+++ b/trend-component-13a/example.mod
@@ -0,0 +1,74 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey g;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
+
+pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+    var g = 0.1;
+end;
+
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
+if ~isequal(M_.pac.pacman.ec.isendo, [false, true])
+   error('ec.isendo vector is wrong.')
+end
diff --git a/trend-component-13b/clean b/trend-component-13b/clean
new file mode 100755
index 000000000..bdc7da19a
--- /dev/null
+++ b/trend-component-13b/clean
@@ -0,0 +1,6 @@
+#!/bin/sh
+
+rm -rf example
+rm  -rf +example
+rm -f example.log
+rm -f *.mat
\ No newline at end of file
diff --git a/trend-component-13b/example.mod b/trend-component-13b/example.mod
new file mode 100644
index 000000000..a2f920dc2
--- /dev/null
+++ b/trend-component-13b/example.mod
@@ -0,0 +1,74 @@
+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey g;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], trends=['eq:x1bar', 'eq:x2bar']);
+
+pac_model(auxiliary_model_name=toto, discount=beta, growth=g, model_name=pacman);
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = e_c_m*(z(-1)-x1(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+    var g = 0.1;
+end;
+
+// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
+pac.initialize('pacman');
+
+if ~isequal(M_.pac.pacman.ec.isendo, [true, false])
+   error('ec.isendo vector is wrong.')
+end

From df0c15d418a4e3f308ea11c9d0ef8d3b4ef3e83d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian?= <stepan@dynare.org>
Date: Thu, 6 Sep 2018 21:02:16 +0000
Subject: [PATCH 55/56] Add LICENSE

---
 LICENSE | 674 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 674 insertions(+)
 create mode 100644 LICENSE

diff --git a/LICENSE b/LICENSE
new file mode 100644
index 000000000..706edf868
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,674 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
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+    Copyright (C) 2018  Stéphane Adjemian
+
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From 72dda0e3ebdb46b741e484f2e2f2155d02c59815 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Thu, 6 Sep 2018 23:13:14 +0200
Subject: [PATCH 56/56] Added README file.

---
 README.md | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 README.md

diff --git a/README.md b/README.md
new file mode 100644
index 000000000..a4a302bbd
--- /dev/null
+++ b/README.md
@@ -0,0 +1,29 @@
+Collection of `*.mod` files for testing the PAC routines in Dynare. To run all the tests sequentially and check that all the `*.mod` files pass the tests, just use the matlab function in the base directory:
+
+```matlab
+>> run_all_tests()
+```
+
+If all goes well, the output should terminate with something like:
+
+```example
+Testsuite results (PAC model):
+
+var-1		             PASS (2.0479s)
+var-2		             PASS (1.9601s)
+var-3		             PASS (1.9826s)
+var-4		             PASS (2.0079s)
+trend-component-1		 PASS (2.2214s)
+trend-component-2		 PASS (2.2195s)
+trend-component-3		 PASS (2.3003s)
+trend-component-4		 PASS (10.5143s)
+trend-component-5		 PASS (2.1538s)
+trend-component-6		 PASS (2.4203s)
+trend-component-7		 PASS (2.7112s)
+trend-component-9		 PASS (2.2164s)
+trend-component-10		 PASS (2.2593s)
+trend-component-11		 PASS (0.69409s)
+trend-component-12		 PASS (2.2663s)
+trend-component-13a		 PASS (0.4119s)
+trend-component-13b		 PASS (0.39554s)
+```