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var_forecast: use example1 in forecast, add code to use estimation via rfvar3

time-shift
Houtan Bastani 2016-11-24 12:34:52 +01:00 committed by Stéphane Adjemian (Charybdis)
parent d46d107837
commit dc7fca7ece
5 changed files with 262 additions and 118 deletions
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105
matlab/bvar_toolbox.m
View File

@ -216,108 +216,3 @@ dimy = size(ydum);
ydum = reshape(permute(ydum,[1 3 2]),dimy(1)*dimy(3),nv);
xdum = reshape(permute(xdum,[1 3 2]),dimy(1)*dimy(3),nx);
breaks = breaks(1:(end-1));
function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu)
%function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu)
% This algorithm goes for accuracy without worrying about memory requirements.
% ydata: dependent variable data matrix
% xdata: exogenous variable data matrix
% lags: number of lags
% breaks: rows in ydata and xdata after which there is a break. This allows for
% discontinuities in the data (e.g. war years) and for the possibility of
% adding dummy observations to implement a prior. This must be a column vector.
% Note that a single dummy observation becomes lags+1 rows of the data matrix,
% with a break separating it from the rest of the data. The function treats the
% first lags observations at the top and after each "break" in ydata and xdata as
% initial conditions.
% lambda: weight on "co-persistence" prior dummy observations. This expresses
% belief that when data on *all* y's are stable at their initial levels, they will
% tend to persist at that level. lambda=5 is a reasonable first try. With lambda<0,
% constant term is not included in the dummy observation, so that stationary models
% with means equal to initial ybar do not fit the prior mean. With lambda>0, the prior
% implies that large constants are unlikely if unit roots are present.
% mu: weight on "own persistence" prior dummy observation. Expresses belief
% that when y_i has been stable at its initial level, it will tend to persist
% at that level, regardless of the values of other variables. There is
% one of these for each variable. A reasonable first guess is mu=2.
% The program assumes that the first lags rows of ydata and xdata are real data, not dummies.
% Dummy observations should go at the end, if any. If pre-sample x's are not available,
% repeating the initial xdata(lags+1,:) row or copying xdata(lags+1:2*lags,:) into
% xdata(1:lags,:) are reasonable subsititutes. These values are used in forming the
% persistence priors.
% Original file downloaded from:
% http://sims.princeton.edu/yftp/VARtools/matlab/rfvar3.m
[T,nvar] = size(ydata);
nox = isempty(xdata);
if ~nox
[T2,nx] = size(xdata);
else
T2 = T;
nx = 0;
xdata = zeros(T2,0);
end
% note that x must be same length as y, even though first part of x will not be used.
% This is so that the lags parameter can be changed without reshaping the xdata matrix.
if T2 ~= T, error('Mismatch of x and y data lengths'),end
if nargin < 4
nbreaks = 0;
breaks = [];
else
nbreaks = length(breaks);
end
breaks = [0;breaks;T];
smpl = [];
for nb = 1:nbreaks+1
smpl = [smpl;[breaks(nb)+lags+1:breaks(nb+1)]'];
end
Tsmpl = size(smpl,1);
X = zeros(Tsmpl,nvar,lags);
for is = 1:length(smpl)
X(is,:,:) = ydata(smpl(is)-(1:lags),:)';
end
X = [X(:,:) xdata(smpl,:)];
y = ydata(smpl,:);
% Everything now set up with input data for y=Xb+e
% Add persistence dummies
if lambda ~= 0 || mu > 0
ybar = mean(ydata(1:lags,:),1);
if ~nox
xbar = mean(xdata(1:lags,:),1);
else
xbar = [];
end
if lambda ~= 0
if lambda>0
xdum = lambda*[repmat(ybar,1,lags) xbar];
else
lambda = -lambda;
xdum = lambda*[repmat(ybar,1,lags) zeros(size(xbar))];
end
ydum = zeros(1,nvar);
ydum(1,:) = lambda*ybar;
y = [y;ydum];
X = [X;xdum];
end
if mu>0
xdum = [repmat(diag(ybar),1,lags) zeros(nvar,nx)]*mu;
ydum = mu*diag(ybar);
X = [X;xdum];
y = [y;ydum];
end
end
% Compute OLS regression and residuals
[vl,d,vr] = svd(X,0);
di = 1./diag(d);
B = (vr.*repmat(di',nvar*lags+nx,1))*vl'*y;
u = y-X*B;
xxi = vr.*repmat(di',nvar*lags+nx,1);
xxi = xxi*xxi';
var.B = B;
var.u = u;
var.xxi = xxi;

122
matlab/rfvar3.m Normal file
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@ -0,0 +1,122 @@
function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu)
%function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu)
% This algorithm goes for accuracy without worrying about memory requirements.
% ydata: dependent variable data matrix
% xdata: exogenous variable data matrix
% lags: number of lags
% breaks: rows in ydata and xdata after which there is a break. This allows for
% discontinuities in the data (e.g. war years) and for the possibility of
% adding dummy observations to implement a prior. This must be a column vector.
% Note that a single dummy observation becomes lags+1 rows of the data matrix,
% with a break separating it from the rest of the data. The function treats the
% first lags observations at the top and after each "break" in ydata and xdata as
% initial conditions.
% lambda: weight on "co-persistence" prior dummy observations. This expresses
% belief that when data on *all* y's are stable at their initial levels, they will
% tend to persist at that level. lambda=5 is a reasonable first try. With lambda<0,
% constant term is not included in the dummy observation, so that stationary models
% with means equal to initial ybar do not fit the prior mean. With lambda>0, the prior
% implies that large constants are unlikely if unit roots are present.
% mu: weight on "own persistence" prior dummy observation. Expresses belief
% that when y_i has been stable at its initial level, it will tend to persist
% at that level, regardless of the values of other variables. There is
% one of these for each variable. A reasonable first guess is mu=2.
% The program assumes that the first lags rows of ydata and xdata are real data, not dummies.
% Dummy observations should go at the end, if any. If pre-sample x's are not available,
% repeating the initial xdata(lags+1,:) row or copying xdata(lags+1:2*lags,:) into
% xdata(1:lags,:) are reasonable subsititutes. These values are used in forming the
% persistence priors.
% Original file downloaded from:
% http://sims.princeton.edu/yftp/VARtools/matlab/rfvar3.m
% Copyright (C) 2003-2007 Christopher Sims
% Copyright (C) 2007-2012 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/>.
[T,nvar] = size(ydata);
nox = isempty(xdata);
if ~nox
[T2,nx] = size(xdata);
else
T2 = T;
nx = 0;
xdata = zeros(T2,0);
end
% note that x must be same length as y, even though first part of x will not be used.
% This is so that the lags parameter can be changed without reshaping the xdata matrix.
if T2 ~= T, error('Mismatch of x and y data lengths'),end
if nargin < 4
nbreaks = 0;
breaks = [];
else
nbreaks = length(breaks);
end
breaks = [0;breaks;T];
smpl = [];
for nb = 1:nbreaks+1
smpl = [smpl;[breaks(nb)+lags+1:breaks(nb+1)]'];
end
Tsmpl = size(smpl,1);
X = zeros(Tsmpl,nvar,lags);
for is = 1:length(smpl)
X(is,:,:) = ydata(smpl(is)-(1:lags),:)';
end
X = [X(:,:) xdata(smpl,:)];
y = ydata(smpl,:);
% Everything now set up with input data for y=Xb+e
% Add persistence dummies
if lambda ~= 0 || mu > 0
ybar = mean(ydata(1:lags,:),1);
if ~nox
xbar = mean(xdata(1:lags,:),1);
else
xbar = [];
end
if lambda ~= 0
if lambda>0
xdum = lambda*[repmat(ybar,1,lags) xbar];
else
lambda = -lambda;
xdum = lambda*[repmat(ybar,1,lags) zeros(size(xbar))];
end
ydum = zeros(1,nvar);
ydum(1,:) = lambda*ybar;
y = [y;ydum];
X = [X;xdum];
end
if mu>0
xdum = [repmat(diag(ybar),1,lags) zeros(nvar,nx)]*mu;
ydum = mu*diag(ybar);
X = [X;xdum];
y = [y;ydum];
end
end
% Compute OLS regression and residuals
[vl,d,vr] = svd(X,0);
di = 1./diag(d);
B = (vr.*repmat(di',nvar*lags+nx,1))*vl'*y;
u = y-X*B;
xxi = vr.*repmat(di',nvar*lags+nx,1);
xxi = xxi*xxi';
var.B = B;
var.u = u;
var.xxi = xxi;
end

51
tests/ECB/example1.mod Normal file
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@ -0,0 +1,51 @@
// Example 1 from Collard's guide to Dynare
var y, c, k, a, h, b;
varexo e, u;
verbatim;
% I want these comments included in
% example1.m 1999q1 1999y
%
var = 1;
end;
parameters beta, rho, alpha, delta, theta, psi, tau;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
k = exp(b)*(y-c)+(1-delta)*k(-1);
a = rho*a(-1)+tau*b(-1) + e;
b = tau*a(-1)+rho*b(-1) + u;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
a = 0;
b = 0;
e = 0;
u = 0;
end;
shocks;
var e; stderr 0.009;
var u; stderr 0.009;
var e, u = phi*0.009*0.009;
end;
stoch_simul(order=1, periods=200);

53
tests/ECB/example1_var.mod Normal file
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@ -0,0 +1,53 @@
// Example 1 from Collard's guide to Dynare
var y, c, k, a, h, b;
varexo e, u;
verbatim;
% I want these comments included in
% example1.m 1999q1 1999y
%
var = 1;
end;
parameters beta, rho, alpha, delta, theta, psi, tau;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
var_model(model_name=my_var_est, order=1) y c;
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(b)*c)/(exp(b(+1))*c(1)))
*(exp(b(+1))*alpha*var_expectation(y, model_name=my_var_est)+(1-delta)*k));
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
k = exp(b)*(y-c)+(1-delta)*k(-1);
a = rho*a(-1)+tau*b(-1) + e;
b = tau*a(-1)+rho*b(-1) + u;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
a = 0;
b = 0;
e = 0;
u = 0;
end;
shocks;
var e; stderr 0.009;
var u; stderr 0.009;
var e, u = phi*0.009*0.009;
end;
stoch_simul(order=1, periods=200);

49
tests/ECB/run_var_comparison.m
View File

@ -1,30 +1,45 @@
clearvars
clearvars -global
close all
!rm nkm_saved_data.mat
!rm my_var_est.mat
!rm nkm_var_saved_data.mat
%% Call Dynare without VAR
dynare nkm.mod
dynare example1.mod
save('nkm_saved_data.mat')
%% Estimate VAR using simulated data
disp('VAR Estimation');
Y = oo_.endo_simul(2:3, 2:end);
Z = [ones(1, size(Y,2)); oo_.endo_simul(2:3, 1:end-1)];
% OLS
B = Y*transpose(Z)/(Z*transpose(Z));
%% save values
% MLS estimate of mu and B (autoregressive_matrices)
% Y = mu + B*Z
% from New Introduction to Multiple Time Series Analysis
Y = oo_.endo_simul(1:2, 2:end);
Z = [ ...
ones(1, size(Y,2)); ...
oo_.endo_simul(1:2, 1:end-1); ...
];
%B = Y*Z'*inv(Z*Z');
B = Y*Z'/(Z*Z');
mu = B(:, 1);
autoregressive_matrices{1} = B(:, 2:end);
% Sims
% (provides same result as above)
% var = rfvar3(Y',1,zeros(size(Y')),0,5,2)
% mu = var.B(:, 1);
% autoregressive_matrices{1} = var.B(:, 2:end);
%% save values
save('my_var_est.mat', 'mu', 'autoregressive_matrices');
%% Call Dynare with VAR
clearvars
clearvars -global
dynare nkm_var.mod
dynare example1_var.mod
save('nkm_var_saved_data.mat')
%% compare values
@ -35,11 +50,19 @@ zerotol = 1e-12;
nv = load('nkm_saved_data.mat');
wv = load('nkm_var_saved_data.mat');
assert(max(max(abs(nv.y - wv.y))) < zerotol);
assert(max(max(abs(nv.pi - wv.pi))) < zerotol);
assert(max(max(abs(nv.i - wv.i))) < zerotol);
ridx = 3;
cidx = 2;
exo_names = nv.M_.exo_names;
endo_names = nv.M_.endo_names;
fn = fieldnames(nv.oo_.irfs);
for i=1:length(fn)
assert(max(max(abs(nv.oo_.irfs.(fn{i}) - (wv.oo_.irfs.(fn{i}))))) < zerotol);
for i = 1:length(exo_names)
figure('Name', ['Shock to ' exo_names(i)]);
for j = 1:length(endo_names)
subplot(ridx, cidx, j);
hold on
title(endo_names(j));
plot(nv.oo_.irfs.([endo_names(j) '_' exo_names(i)]));
plot(wv.oo_.irfs.([endo_names(j) '_' exo_names(i)]), '--');
hold off
end
end