v4.1: Changes related to (posterior) 2nd order moments.
+ Efficiency changes: ++ Do not compute the variance decomposition if not needed. ++ Do not apply the Schur decomposition for each shock in case of a variance decomposition. + Bug corrections and cosmetic changes. + Corrections of some headers. git-svn-id: https://www.dynare.org/svn/dynare/trunk@2411 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
stepan
parent
91264b696f
commit
fe418672cd
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@ -51,7 +51,7 @@ function oo_ = compute_moments_varendo(options_,M_,oo_,var_list_)
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end
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% VARIANCE DECOMPOSITION.
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for i=1:NumberOfEndogenousVariables
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for j=i:NumberOfExogenousVariables
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for j=1:NumberOfExogenousVariables
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oo_ = posterior_analysis('decomposition',var_list_(i,:),M_.exo_names(j,:),[],options_,M_,oo_);
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end
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end
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@ -20,7 +20,7 @@ function [nvar,vartan,CorrFileNumber] = dsge_posterior_theoretical_correlation(S
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% th_autocovariances.m
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% posterior_moments.m
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% Copyright (C) 2007-2008 Dynare Team
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% Copyright (C) 2007-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -38,6 +38,7 @@ function [nvar,vartan,CorrFileNumber] = dsge_posterior_theoretical_correlation(S
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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type = 'posterior';
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nodecomposition = 1;
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% Set varlist (vartan)
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[ivar,vartan] = set_stationary_variables_list;
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@ -80,7 +81,7 @@ for file = 1:NumberOfDrawsFiles
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set_parameters(pdraws{linee,1});
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[dr,info] = resol(oo_.steady_state,0);
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end
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tmp = th_autocovariances(dr,ivar,M_,options_);
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tmp = th_autocovariances(dr,ivar,M_,options_,nodecomposition);
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for i=1:nar
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Correlation_array(linea,:,:,i) = tmp{i+1};
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end
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@ -19,7 +19,7 @@ function [nvar,vartan,CovarFileNumber] = dsge_posterior_theoretical_covariance(S
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% th_autocovariances.m
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% posterior_moments.m
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% Copyright (C) 2007-2008 Dynare Team
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% Copyright (C) 2007-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -37,7 +37,8 @@ function [nvar,vartan,CovarFileNumber] = dsge_posterior_theoretical_covariance(S
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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type = 'posterior';
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nodecomposition = 1;
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% Set varlist (vartan)
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[ivar,vartan] = set_stationary_variables_list;
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nvar = length(ivar);
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@ -79,7 +80,7 @@ for file = 1:NumberOfDrawsFiles
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set_parameters(pdraws{linee,1});
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[dr,info] = resol(oo_.steady_state,0);
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end
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tmp = th_autocovariances(dr,ivar,M_,options_);
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tmp = th_autocovariances(dr,ivar,M_,options_,nodecomposition);
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for i=1:nvar
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for j=i:nvar
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Covariance_matrix(linea,symmetric_matrix_index(i,j,nvar)) = tmp{1}(i,j);
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@ -94,7 +95,7 @@ for file = 1:NumberOfDrawsFiles
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Covariance_matrix = zeros(NumberOfLinesInTheLastCovarFile,nvar*(nvar+1)/2);
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NumberOfCovarLines = NumberOfLinesInTheLastCovarFile;
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CovarFileNumber = CovarFileNumber - 1;
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elseif test<0;
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elseif test<0
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Covariance_matrix = zeros(MaXNumberOfCovarLines,nvar*(nvar+1)/2);
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else
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clear('Covariance_matrix');
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@ -18,7 +18,7 @@ function [nvar,vartan,NumberOfDecompFiles] = ...
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% th_autocovariances.m
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% posterior_moments.m
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% Copyright (C) 2007-2008 Dynare Team
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% Copyright (C) 2007-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -36,6 +36,7 @@ function [nvar,vartan,NumberOfDecompFiles] = ...
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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type = 'posterior';% To be defined as a input argument later...
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nodecomposition = 0;
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% Set varlist (vartan)
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[ivar,vartan] = set_stationary_variables_list;
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@ -51,7 +52,6 @@ NumberOfDrawsFiles = length(DrawsFiles);
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nexo = M_.exo_nbr;
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NumberOfDrawsFiles = rows(DrawsFiles);
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NumberOfSavedElementsPerSimulation = nvar*(nexo+1);
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MaXNumberOfDecompLines = ceil(options_.MaxNumberOfBytes/NumberOfSavedElementsPerSimulation/8);
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@ -84,7 +84,7 @@ for file = 1:NumberOfDrawsFiles
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set_parameters(pdraws{linee,1});
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[dr,info] = resol(oo_.steady_state,0);
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end
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tmp = th_autocovariances(dr,ivar,M_,options_);
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tmp = th_autocovariances(dr,ivar,M_,options_,nodecomposition);
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for i=1:nvar
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for j=1:nexo
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Decomposition_array(linea,(i-1)*nexo+j) = tmp{2}(i,j);
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@ -1,24 +1,24 @@
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function [x,u]=lyapunov_symm(a,b,qz_criterium)
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% Solves the Lyapunov equation x-a*x*a' = b, for b (and then x) symmetrical
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% if a has some unit roots, the function computes only the solution of the stable subsystem
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function [x,u] = lyapunov_symm(a,b,qz_criterium,method)
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% Solves the Lyapunov equation x-a*x*a' = b, for b and x symmetric matrices.
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% If a has some unit roots, the function computes only the solution of the stable subsystem.
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%
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% INPUTS:
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% a: coefficient matrix (n x n)
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% b: coefficient square matrix (n x n)
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%
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% a [double] n*n matrix.
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% b [double] n*n matrix
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% method [integer] Scalar, if method=0 [default] then U, T, n and k are not persistent.
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% method=1 then U, T, n and k are declared as persistent variables and the schur decomposition is triggered.
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% method=2 then U, T, n and k are declared as persistent variables and the schur decomposition is not performed.
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% OUTPUTS
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% x: solution matrix (m x m)
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% ns_var: vector of indices of non-stationary variables (p x 1)
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% (m + p = n)
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% u: Schur vectors associated with unit roots
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% x: [double] m*m solution matrix of the lyapunov equation, where m is the dimension of the stable subsystem.
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% u: [double] Schur vectors associated with unit roots
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%
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% ALGORITHM
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% uses reordered Schur decomposition
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% Uses reordered Schur decomposition
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%
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% SPECIAL REQUIREMENTS
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% needs Matlab >= 7.0.1 for ordeig function (otherwise uses my_ordeig)
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% Copyright (C) 2006-2008 Dynare Team
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% Copyright (C) 2006-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -34,76 +34,90 @@ function [x,u]=lyapunov_symm(a,b,qz_criterium)
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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ns_var = [];
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u = [];
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info = 0;
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if size(a,1) == 1
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x=b/(1-a*a);
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return
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end
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[u,t] = schur(a);
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if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
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e1 = abs(my_ordeig(t)) > 2-qz_criterium;
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else
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e1 = abs(ordeig(t)) > 2-qz_criterium;
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end
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k = sum(e1);
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if exist('ordschur','builtin')
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% selects stable roots
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[u,t] = ordschur(u,t,e1);
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n = length(e1)-k;
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b=u(:,k+1:end)'*b*u(:,k+1:end);
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t = t(k+1:end,k+1:end);
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elseif k > 0
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% problem for Matlab version that don't have ordschur
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error(['lyapunov_sym: you need a Matlab version > 6.5 to handle models' ...
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' with unit roots'])
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else
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% no unit root
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n = length(e1);
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b=u'*b*u;
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end
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x=zeros(n,n);
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i = n;
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while i >= 2
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if t(i,i-1) == 0
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if i == n
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c = zeros(n,1);
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else
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c = t(1:i,:)*(x(:,i+1:end)*t(i,i+1:end)')+...
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t(i,i)*t(1:i,i+1:end)*x(i+1:end,i);
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end
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q = eye(i)-t(1:i,1:i)*t(i,i);
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x(1:i,i) = q\(b(1:i,i)+c);
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x(i,1:i-1) = x(1:i-1,i)';
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i = i - 1;
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else
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if i == n
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c = zeros(n,1);
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c1 = zeros(n,1);
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else
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c = t(1:i,:)*(x(:,i+1:end)*t(i,i+1:end)')+...
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t(i,i)*t(1:i,i+1:end)*x(i+1:end,i)+...
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t(i,i-1)*t(1:i,i+1:end)*x(i+1:end,i-1);
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c1 = t(1:i,:)*(x(:,i+1:end)*t(i-1,i+1:end)')+...
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t(i-1,i-1)*t(1:i,i+1:end)*x(i+1:end,i-1)+...
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t(i-1,i)*t(1:i,i+1:end)*x(i+1:end,i);
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end
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q = [eye(i)-t(1:i,1:i)*t(i,i) -t(1:i,1:i)*t(i,i-1);...
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-t(1:i,1:i)*t(i-1,i) eye(i)-t(1:i,1:i)*t(i-1,i-1)];
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z = q\[b(1:i,i)+c;b(1:i,i-1)+c1];
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x(1:i,i) = z(1:i);
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x(1:i,i-1) = z(i+1:end);
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x(i,1:i-1)=x(1:i-1,i)';
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x(i-1,1:i-2)=x(1:i-2,i-1)';
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i = i - 2;
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if nargin<4
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method = 0;
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end
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end
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if i == 1
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c = t(1,:)*(x(:,2:end)*t(1,2:end)')+t(1,1)*t(1,2:end)*x(2:end,1);
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x(1,1)=(b(1,1)+c)/(1-t(1,1)*t(1,1));
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end
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x = u(:,k+1:end)*x*u(:,k+1:end)';
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u = u(:,1:k);
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if method
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persistent U T k n
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else
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if exist('U','var')
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clear('U','T','k','n')
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end
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end
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u = [];
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if size(a,1) == 1
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x=b/(1-a*a);
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return
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end
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if method<2
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[U,T] = schur(a);
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if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
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e1 = abs(my_ordeig(T)) > 2-qz_criterium;
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else
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e1 = abs(ordeig(T)) > 2-qz_criterium;
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end
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k = sum(e1); % Number of unit roots.
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n = length(e1)-k; % Number of stationary variables.
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if exist('ordschur','builtin')
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% Selects stable roots
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[U,T] = ordschur(U,T,e1);
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% B = U(:,k+1:end)'*b*U(:,k+1:end);
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T = T(k+1:end,k+1:end);
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elseif k > 0
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% Problem for Matlab version that don't have ordschur
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error(['lyapunov_sym: you need a Matlab version > 6.5 to handle models' ...
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' with unit roots'])
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%else
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% No unit root
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%n = length(e1);
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%B=u'*b*u;
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end
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end
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B = U(:,k+1:end)'*b*U(:,k+1:end);
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x = zeros(n,n);
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i = n;
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while i >= 2
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if T(i,i-1) == 0
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if i == n
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c = zeros(n,1);
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else
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c = T(1:i,:)*(x(:,i+1:end)*T(i,i+1:end)') + ...
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T(i,i)*T(1:i,i+1:end)*x(i+1:end,i);
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end
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q = eye(i)-T(1:i,1:i)*T(i,i);
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x(1:i,i) = q\(B(1:i,i)+c);
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x(i,1:i-1) = x(1:i-1,i)';
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i = i - 1;
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else
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if i == n
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c = zeros(n,1);
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c1 = zeros(n,1);
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else
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c = T(1:i,:)*(x(:,i+1:end)*T(i,i+1:end)') + ...
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T(i,i)*T(1:i,i+1:end)*x(i+1:end,i) + ...
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T(i,i-1)*T(1:i,i+1:end)*x(i+1:end,i-1);
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c1 = T(1:i,:)*(x(:,i+1:end)*T(i-1,i+1:end)') + ...
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T(i-1,i-1)*T(1:i,i+1:end)*x(i+1:end,i-1) + ...
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T(i-1,i)*T(1:i,i+1:end)*x(i+1:end,i);
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end
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q = [eye(i)-T(1:i,1:i)*T(i,i) - T(1:i,1:i)*T(i,i-1) ; ...
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-T(1:i,1:i)*T(i-1,i) eye(i) - T(1:i,1:i)*T(i-1,i-1) ];
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z = q\[ B(1:i,i)+c ; B(1:i,i-1) + c1 ];
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x(1:i,i) = z(1:i);
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x(1:i,i-1) = z(i+1:end);
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x(i,1:i-1) = x(1:i-1,i)';
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x(i-1,1:i-2) = x(1:i-2,i-1)';
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i = i - 2;
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end
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end
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if i == 1
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c = T(1,:)*(x(:,2:end)*T(1,2:end)') + T(1,1)*T(1,2:end)*x(2:end,1);
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x(1,1) = (B(1,1)+c)/(1-T(1,1)*T(1,1));
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end
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x = U(:,k+1:end)*x*U(:,k+1:end)';
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u = U(:,1:k);
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@ -1,22 +1,30 @@
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function [Gamma_y,ivar]=th_autocovariances(dr,ivar,M_,options_)
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function [Gamma_y,ivar] = th_autocovariances(dr,ivar,M_,options_,nodecomposition)
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% Computes the theoretical auto-covariances, Gamma_y, for an AR(p) process
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% with coefficients dr.ghx and dr.ghu and shock variances Sigma_e_
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% for a subset of variables ivar (indices in lgy_)
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%
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% Theoretical HPfiltering is available as an option
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%
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% INPUTS
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% dr: structure of decisions rules for stochastic simulations
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% ivar: subset of variables
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% M_
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% options_
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% dr: [structure] Reduced form solution of the DSGE model (decisions rules)
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% ivar: [integer] Vector of indices for a subset of variables.
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% M_ [structure] Global dynare's structure, description of the DSGE model.
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% options_ [structure] Global dynare's structure.
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% nodecomposition [integer] Scalar, if different from zero the variance decomposition is not triggered.
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%
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% OUTPUTS
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% Gamma_y: theoritical auto-covariances
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% ivar: subset of variables
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% Gamma_y [cell] Matlab cell of nar+3 (second order approximation) or nar+2 (first order approximation) arrays,
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% where nar is the order of the autocorrelation function.
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% Gamma_y{1} [double] Covariance matrix.
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% Gamma_y{i} [double] Autocorrelation function (for i=1,...,options_.nar).
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% Gamma_y{nar+2} [double] Variance decomposition.
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% Gamma_y{nar+3} [double] Expectation of the endogenous variables associated with a second
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% order approximation.
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% ivar [integer] Vector of indices for a subset of variables.
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%
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% SPECIAL REQUIREMENTS
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% Theoretical HP filtering is available as an option
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%
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% Copyright (C) 2001-2008 Dynare Team
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% Copyright (C) 2001-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -33,188 +41,181 @@ function [Gamma_y,ivar]=th_autocovariances(dr,ivar,M_,options_)
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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exo_names_orig_ord = M_.exo_names_orig_ord;
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if exist('OCTAVE_VERSION')
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warning('off', 'Octave:divide-by-zero')
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else
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warning off MATLAB:dividebyzero
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end
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nar = options_.ar;
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Gamma_y = cell(nar+1,1);
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if isempty(ivar)
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ivar = [1:M_.endo_nbr]';
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end
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nvar = size(ivar,1);
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if nargin<5
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nodecomposition = 0;
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end
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exo_names_orig_ord = M_.exo_names_orig_ord;
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if exist('OCTAVE_VERSION')
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warning('off', 'Octave:divide-by-zero')
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else
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warning off MATLAB:dividebyzero
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end
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nar = options_.ar;
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Gamma_y = cell(nar+1,1);
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if isempty(ivar)
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ivar = [1:M_.endo_nbr]';
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end
|
||||
nvar = size(ivar,1);
|
||||
|
||||
ghx = dr.ghx;
|
||||
ghu = dr.ghu;
|
||||
npred = dr.npred;
|
||||
nstatic = dr.nstatic;
|
||||
kstate = dr.kstate;
|
||||
order = dr.order_var;
|
||||
iv(order) = [1:length(order)];
|
||||
nx = size(ghx,2);
|
||||
ghx = dr.ghx;
|
||||
ghu = dr.ghu;
|
||||
npred = dr.npred;
|
||||
nstatic = dr.nstatic;
|
||||
kstate = dr.kstate;
|
||||
order = dr.order_var;
|
||||
iv(order) = [1:length(order)];
|
||||
nx = size(ghx,2);
|
||||
|
||||
ikx = [nstatic+1:nstatic+npred];
|
||||
ikx = [nstatic+1:nstatic+npred];
|
||||
|
||||
k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
|
||||
i0 = find(k0(:,2) == M_.maximum_lag+1);
|
||||
i00 = i0;
|
||||
n0 = length(i0);
|
||||
AS = ghx(:,i0);
|
||||
ghu1 = zeros(nx,M_.exo_nbr);
|
||||
ghu1(i0,:) = ghu(ikx,:);
|
||||
for i=M_.maximum_lag:-1:2
|
||||
i1 = find(k0(:,2) == i);
|
||||
n1 = size(i1,1);
|
||||
j1 = zeros(n1,1);
|
||||
for k1 = 1:n1
|
||||
j1(k1) = find(k0(i00,1)==k0(i1(k1),1));
|
||||
k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
|
||||
i0 = find(k0(:,2) == M_.maximum_lag+1);
|
||||
i00 = i0;
|
||||
n0 = length(i0);
|
||||
AS = ghx(:,i0);
|
||||
ghu1 = zeros(nx,M_.exo_nbr);
|
||||
ghu1(i0,:) = ghu(ikx,:);
|
||||
for i=M_.maximum_lag:-1:2
|
||||
i1 = find(k0(:,2) == i);
|
||||
n1 = size(i1,1);
|
||||
j1 = zeros(n1,1);
|
||||
for k1 = 1:n1
|
||||
j1(k1) = find(k0(i00,1)==k0(i1(k1),1));
|
||||
end
|
||||
AS(:,j1) = AS(:,j1)+ghx(:,i1);
|
||||
i0 = i1;
|
||||
end
|
||||
AS(:,j1) = AS(:,j1)+ghx(:,i1);
|
||||
i0 = i1;
|
||||
end
|
||||
b = ghu1*M_.Sigma_e*ghu1';
|
||||
|
||||
|
||||
ipred = nstatic+(1:npred)';
|
||||
% state space representation for state variables only
|
||||
[A,B] = kalman_transition_matrix(dr,ipred,1:nx,dr.transition_auxiliary_variables,M_.exo_nbr);
|
||||
if options_.order == 2 | options_.hp_filter == 0
|
||||
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium);
|
||||
iky = iv(ivar);
|
||||
if ~isempty(u)
|
||||
iky = iky(find(all(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));
|
||||
ivar = dr.order_var(iky);
|
||||
end
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
if options_.order == 2 % mean correction for 2nd order
|
||||
Ex = (dr.ghs2(ikx)+dr.ghxx(ikx,:)*vx(:)+dr.ghuu(ikx,:)*M_.Sigma_e(:))/2;
|
||||
Ex = (eye(n0)-AS(ikx,:))\Ex;
|
||||
Gamma_y{nar+3} = AS(iky,:)*Ex+(dr.ghs2(iky)+dr.ghxx(iky,:)*vx(:)+...
|
||||
dr.ghuu(iky,:)*M_.Sigma_e(:))/2;
|
||||
end
|
||||
end
|
||||
if options_.hp_filter == 0
|
||||
Gamma_y{1} = aa*vx*aa'+ bb*M_.Sigma_e*bb';
|
||||
k = find(abs(Gamma_y{1}) < 1e-12);
|
||||
Gamma_y{1}(k) = 0;
|
||||
b = ghu1*M_.Sigma_e*ghu1';
|
||||
|
||||
% autocorrelations
|
||||
if nar > 0
|
||||
vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
|
||||
|
||||
sy = sqrt(diag(Gamma_y{1}));
|
||||
sy = sy *sy';
|
||||
Gamma_y{2} = aa*vxy./sy;
|
||||
|
||||
for i=2:nar
|
||||
vxy = A*vxy;
|
||||
Gamma_y{i+1} = aa*vxy./sy;
|
||||
end
|
||||
end
|
||||
|
||||
% variance decomposition
|
||||
if M_.exo_nbr > 1
|
||||
Gamma_y{nar+2} = zeros(length(ivar),M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord)=M_.Sigma_e+1e-14*eye(M_.exo_nbr);
|
||||
cs = chol(SS)';
|
||||
b1(:,exo_names_orig_ord) = ghu1;
|
||||
b1 = b1*cs;
|
||||
b2(:,exo_names_orig_ord) = ghu(iky,:);
|
||||
b2 = b2*cs;
|
||||
vx = lyapunov_symm(A,b1*b1',options_.qz_criterium);
|
||||
vv = diag(aa*vx*aa'+b2*b2');
|
||||
for i=1:M_.exo_nbr
|
||||
vx1 = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.qz_criterium);
|
||||
Gamma_y{nar+2}(:,i) = abs(diag(aa*vx1*aa'+b2(:,i)*b2(:,i)'))./vv;
|
||||
end
|
||||
ipred = nstatic+(1:npred)';
|
||||
% state space representation for state variables only
|
||||
[A,B] = kalman_transition_matrix(dr,ipred,1:nx,dr.transition_auxiliary_variables,M_.exo_nbr);
|
||||
if options_.order == 2 | options_.hp_filter == 0
|
||||
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium);
|
||||
iky = iv(ivar);
|
||||
if ~isempty(u)
|
||||
iky = iky(find(all(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));
|
||||
ivar = dr.order_var(iky);
|
||||
end
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
if options_.order == 2 % mean correction for 2nd order
|
||||
Ex = (dr.ghs2(ikx)+dr.ghxx(ikx,:)*vx(:)+dr.ghuu(ikx,:)*M_.Sigma_e(:))/2;
|
||||
Ex = (eye(n0)-AS(ikx,:))\Ex;
|
||||
Gamma_y{nar+3} = AS(iky,:)*Ex+(dr.ghs2(iky)+dr.ghxx(iky,:)*vx(:)+...
|
||||
dr.ghuu(iky,:)*M_.Sigma_e(:))/2;
|
||||
end
|
||||
end
|
||||
else
|
||||
if options_.order < 2
|
||||
iky = iv(ivar);
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
if options_.hp_filter == 0
|
||||
Gamma_y{1} = aa*vx*aa'+ bb*M_.Sigma_e*bb';
|
||||
k = find(abs(Gamma_y{1}) < 1e-12);
|
||||
Gamma_y{1}(k) = 0;
|
||||
% autocorrelations
|
||||
if nar > 0
|
||||
vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
|
||||
sy = sqrt(diag(Gamma_y{1}));
|
||||
sy = sy *sy';
|
||||
Gamma_y{2} = aa*vxy./sy;
|
||||
for i=2:nar
|
||||
vxy = A*vxy;
|
||||
Gamma_y{i+1} = aa*vxy./sy;
|
||||
end
|
||||
end
|
||||
% variance decomposition
|
||||
if ~nodecomposition && M_.exo_nbr > 1
|
||||
Gamma_y{nar+2} = zeros(length(ivar),M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord)=M_.Sigma_e+1e-14*eye(M_.exo_nbr);
|
||||
cs = chol(SS)';
|
||||
b1(:,exo_names_orig_ord) = ghu1;
|
||||
b1 = b1*cs;
|
||||
b2(:,exo_names_orig_ord) = ghu(iky,:);
|
||||
b2 = b2*cs;
|
||||
vx = lyapunov_symm(A,b1*b1',options_.qz_criterium,1);
|
||||
vv = diag(aa*vx*aa'+b2*b2');
|
||||
for i=1:M_.exo_nbr
|
||||
vx1 = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.qz_criterium,2);
|
||||
Gamma_y{nar+2}(:,i) = abs(diag(aa*vx1*aa'+b2(:,i)*b2(:,i)'))./vv;
|
||||
end
|
||||
end
|
||||
else% ==> Theoretical HP filter.
|
||||
if options_.order < 2
|
||||
iky = iv(ivar);
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
end
|
||||
lambda = options_.hp_filter;
|
||||
ngrid = options_.hp_ngrid;
|
||||
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
|
||||
tpos = exp( sqrt(-1)*freqs);
|
||||
tneg = exp(-sqrt(-1)*freqs);
|
||||
hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
|
||||
mathp_col = [];
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
% Covariance of filtered series
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
Gamma_y{1} = reshape(imathp_col(1,:),nvar,nvar);
|
||||
% Autocorrelations
|
||||
if nar > 0
|
||||
sy = sqrt(diag(Gamma_y{1}));
|
||||
sy = sy *sy';
|
||||
for i=1:nar
|
||||
Gamma_y{i+1} = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
|
||||
end
|
||||
end
|
||||
% Variance decomposition
|
||||
if ~nodecomposition && M_.exo_nbr > 1
|
||||
Gamma_y{nar+2} = zeros(nvar,M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord) = M_.Sigma_e+1e-14*eye(M_.exo_nbr);
|
||||
cs = chol(SS)';
|
||||
SS = cs*cs';
|
||||
b1(:,exo_names_orig_ord) = ghu1;
|
||||
b2(:,exo_names_orig_ord) = ghu(iky,:);
|
||||
mathp_col = [];
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SS*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
vv = diag(reshape(imathp_col(1,:),nvar,nvar));
|
||||
for i=1:M_.exo_nbr
|
||||
mathp_col = [];
|
||||
SSi = cs(:,i)*cs(:,i)';
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SSi*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
Gamma_y{nar+2}(:,i) = abs(diag(reshape(imathp_col(1,:),nvar,nvar)))./vv;
|
||||
end
|
||||
end
|
||||
end
|
||||
lambda = options_.hp_filter;
|
||||
ngrid = options_.hp_ngrid;
|
||||
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
|
||||
tpos = exp( sqrt(-1)*freqs);
|
||||
tneg = exp(-sqrt(-1)*freqs);
|
||||
hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
|
||||
|
||||
mathp_col = [];
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
|
||||
% covariance of filtered series
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
|
||||
Gamma_y{1} = reshape(imathp_col(1,:),nvar,nvar);
|
||||
|
||||
% autocorrelations
|
||||
if nar > 0
|
||||
sy = sqrt(diag(Gamma_y{1}));
|
||||
sy = sy *sy';
|
||||
for i=1:nar
|
||||
Gamma_y{i+1} = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
|
||||
end
|
||||
if exist('OCTAVE_VERSION')
|
||||
warning('on', 'Octave:divide-by-zero')
|
||||
else
|
||||
warning on MATLAB:dividebyzero
|
||||
end
|
||||
|
||||
%variance decomposition
|
||||
if M_.exo_nbr > 1
|
||||
Gamma_y{nar+2} = zeros(nvar,M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord) = M_.Sigma_e+1e-14*eye(M_.exo_nbr);
|
||||
cs = chol(SS)';
|
||||
SS = cs*cs';
|
||||
b1(:,exo_names_orig_ord) = ghu1;
|
||||
b2(:,exo_names_orig_ord) = ghu(iky,:);
|
||||
mathp_col = [];
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SS*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
vv = diag(reshape(imathp_col(1,:),nvar,nvar));
|
||||
for i=1:M_.exo_nbr
|
||||
mathp_col = [];
|
||||
SSi = cs(:,i)*cs(:,i)';
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SSi*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
Gamma_y{nar+2}(:,i) = abs(diag(reshape(imathp_col(1,:),nvar,nvar)))./vv;
|
||||
end
|
||||
end
|
||||
end
|
||||
if exist('OCTAVE_VERSION')
|
||||
warning('on', 'Octave:divide-by-zero')
|
||||
else
|
||||
warning on MATLAB:dividebyzero
|
||||
end
|
||||
|
||||
Loading…
Reference in New Issue