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dynare/matlab/partial_information/PCL_Part_info_moments.m

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function [irfmat,irfst]=PCL_Part_info_moments( H, varobs, dr,ivar)
% sets up parameters and calls part-info kalman filter
% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
% suit partial information RE solution in accordance with, and based on, the
% Pearlman, Currie and Levine 1986 solution.
% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
% Copyright (C) 2001-20010 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/>.
% Recall that the state space is given by the
% predetermined variables s(t-1), x(t-1)
% and the jump variables x(t).
% The jump variables have dimension NETA
global M_ options_ oo_
warning_old_state = warning;
warning off
[junk,OBS] = ismember(varobs,M_.endo_names,'rows');
G1=dr.PI_ghx;
impact=dr.PI_ghu;
nmat=dr.PI_nmat;
CC=dr.PI_CC;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
% NETA=dr.nfwrd+dr.nboth; % total no of exp. errors set to no of forward looking equations
FL_RANK=dr.PI_FL_RANK;
NY=M_.endo_nbr;
if isempty(OBS)
NOBS=NY;
LL=eye(NY,NY);
else %and if no obsevations specify OBS=[0] but this is not going to work properly
NOBS=length(OBS);
LL=zeros(NOBS,NY);
for i=1:NOBS
LL(i,OBS(i))=1;
end
end
if exist( 'irfpers')==1
if ~isempty(irfpers)
if irfpers<=0, irfpers=20, end;
else
irfpers=20;
end
else
irfpers=20;
end
ss=size(G1,1);
pd=ss-size(nmat,1);
SDX=M_.Sigma_e^0.5; % =SD,not V-COV, of Exog shocks or M_.Sigma_e^0.5 num_exog x num_exog matrix
if isempty(H)
H=M_.H;
end
VV=H; % V-COV of observation errors.
MM=impact*SDX; % R*(Q^0.5) in standard KF notation
% observation vector indices
% mapping to endogenous variables.
L1=LL*dr.PI_TT1;
L2=LL*dr.PI_TT2;
MM1=MM(1:ss-FL_RANK,:);
U11=MM1*MM1';
% SDX
U22=0;
% determine K1 and K2 observation mapping matrices
% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
% and s(t) is expressed in the dynamics as
% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
% Thus the observations o(t) can be written in the form
% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
G12=G1(NX+1:ss-2*FL_RANK,:);
KK1=L1*G12;
K1=KK1(:,1:ss-FL_RANK);
K2=KK1(:,ss-FL_RANK+1:ss)+L2;
%pre calculate time-invariant factors
A11=G1(1:pd,1:pd);
A22=G1(pd+1:end, pd+1:end);
A12=G1(1:pd, pd+1:end);
A21=G1(pd+1:end,1:pd);
Lambda= nmat*A12+A22;
%A11_A12Nmat= A11-A12*nmat % test
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
% kf_param structure:
AA=A11-BB*A21;
CCCC=A11-A12*nmat; % F in new notation
DD=K1-FF*A21; % H in new notation
EE=K1-K2*nmat;
RR=FF*UFT+VV;
if ~any(RR)
% if zero add some dummy measurement err. variance-covariances
% with diagonals 0.000001. This would not be needed if we used
% the slow solver, or the generalised eigenvalue approach,
% but these are both slower.
RR=eye(size(RR,1))*1.0e-6;
end
SS=BB*UFT;
VKLUFT=VV+K2*I_L*UFT;
ALUFT=A12*I_L*UFT;
FULKV=FF*U22*I_L'*K2'+VV;
FUBT=FF*U22*BB';
nmat=nmat;
% initialise pshat
AQDS=AA*QQ*DD'+SS;
DQDR=DD*QQ*DD'+RR;
I_DQDR=inv(DQDR);
AQDQ=AQDS*I_DQDR;
ff=AA-AQDQ*DD;
hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
rr=DD*QQ*DD'+RR;
ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
PP=ZSIG0 +QQ;
exo_names=M_.exo_names(M_.exo_names_orig_ord,:);
DPDR=DD*PP*DD'+RR;
I_DPDR=inv(DPDR);
%GG=[ CCCC, zeros(pd,NETA); -nmat*CCCC, zeros(NETA,NETA)];
PDIDPDRD=PP*DD'*I_DPDR*DD;
MSIG=disclyap_fast(CCCC, CCCC*PDIDPDRD*PP*CCCC');
COV_P=[ PP, PP; PP, PP+MSIG]; % P0
dr.PI_GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
GAM= [ AA*(eye(ss-FL_RANK)-PDIDPDRD) zeros(ss-FL_RANK); (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD), CCCC];
VV = [ dr.PI_TT1 dr.PI_TT2];
nn=size(VV,1);
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YR0= VV*COV_OMEGA*VV';
diagCovYR0=diag(COV_YR0);
labels = deblank(M_.endo_names(ivar,:));
if options_.nomoments == 0
z = [ sqrt(diagCovYR0(ivar)) diagCovYR0(ivar) ];
title='MOMENTS OF SIMULATED VARIABLES';
headers=strvcat('VARIABLE','STD. DEV.','VARIANCE');
dyntable(title,headers,labels,z,size(labels,2)+2,16,10);
end
if options_.nocorr == 0
diagSqrtCovYR0=sqrt(diagCovYR0);
%COR_Y= diag(diagSqrtCovYR0)*COV_YR0*diag(diagSqrtCovYR0);
DELTA=inv(diag(diagSqrtCovYR0));
COR_Y= DELTA*COV_YR0*DELTA;
title = 'CORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',M_.endo_names(ivar,:));
dyntable(title,headers,labels,COR_Y(ivar,ivar),size(labels,2)+2,8,4);
else
COR_Y=[];
end
ar = options_.ar;
options_ = set_default_option(options_,'ar',5);
ar = options_.ar;
if ar > 0
COV_YRk= zeros(nn,ar);
AutoCOR_YRk= zeros(nn,ar);
for k=1:ar;
COV_P=GAM*COV_P;
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YRk = VV*COV_OMEGA*VV';
AutoCOR_YRkMAT=DELTA*COV_YRk*DELTA;
oo_.autocorr{k}=AutoCOR_YRkMAT(ivar,ivar);
AutoCOR_YRk(:,k)= diag(COV_YRk)./diagCovYR0;
end
title = 'AUTOCORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',int2str([1:ar]'));
dyntable(title,headers,labels,AutoCOR_YRk(ivar,:),size(labels,2)+2,8,4);
else
AutoCOR_YRk=[];
end
save ([M_.fname '_PCL_moments'], 'COV_YR0','AutoCOR_YRk', 'COR_Y');
warning(warning_old_state);
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