105 lines
4.5 KiB
Matlab
105 lines
4.5 KiB
Matlab
function [ConditionalVarianceDecomposition, ConditionalVarianceDecomposition_ME]= conditional_variance_decomposition(StateSpaceModel, Steps, SubsetOfVariables,sigma_e_is_diagonal)
|
|
% This function computes the conditional variance decomposition of a given state space model
|
|
% for a subset of endogenous variables.
|
|
%
|
|
% INPUTS
|
|
% StateSpaceModel [structure] Specification of the state space model.
|
|
% Steps [integer] 1*h vector of dates.
|
|
% SubsetOfVariables [integer] 1*q vector of indices (declaration order).
|
|
%
|
|
% OUTPUTS
|
|
% ConditionalVarianceDecomposition [double] [n h p] array, where
|
|
% n is equal to length(SubsetOfVariables)
|
|
% h is the number of Steps
|
|
% p is the number of state innovations and
|
|
% ConditionalVarianceDecomposition_ME [double] [m h p] array, where
|
|
% m is equal to length(intersect(SubsetOfVariables,varobs))
|
|
% h is the number of Steps
|
|
% p is the number of state innovations and
|
|
|
|
% Copyright (C) 2010-2021 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/>.
|
|
|
|
if any(Steps <= 0)
|
|
error(['Conditional variance decomposition: All periods must be strictly ' ...
|
|
'positive'])
|
|
end
|
|
|
|
number_of_state_innovations = ...
|
|
StateSpaceModel.number_of_state_innovations;
|
|
transition_matrix = StateSpaceModel.transition_matrix;
|
|
number_of_state_equations = ...
|
|
StateSpaceModel.number_of_state_equations;
|
|
order_var = StateSpaceModel.order_var;
|
|
nSteps = length(Steps);
|
|
|
|
ConditionalVariance = zeros(number_of_state_equations,nSteps,number_of_state_innovations);
|
|
|
|
if StateSpaceModel.sigma_e_is_diagonal
|
|
B = StateSpaceModel.impulse_matrix.* ...
|
|
repmat(sqrt(diag(StateSpaceModel.state_innovations_covariance_matrix)'),...
|
|
number_of_state_equations,1);
|
|
else
|
|
B = StateSpaceModel.impulse_matrix*chol(StateSpaceModel.state_innovations_covariance_matrix)';
|
|
end
|
|
|
|
for i=1:number_of_state_innovations
|
|
BB = B(:,i)*B(:,i)';
|
|
V = zeros(number_of_state_equations,number_of_state_equations);
|
|
m = 1;
|
|
for h = 1:max(Steps)
|
|
V = transition_matrix*V*transition_matrix'+BB;
|
|
if h == Steps(m)
|
|
ConditionalVariance(order_var,m,i) = diag(V);
|
|
m = m+1;
|
|
end
|
|
end
|
|
end
|
|
|
|
ConditionalVariance = ConditionalVariance(SubsetOfVariables,:,:);
|
|
|
|
NumberOfVariables = length(SubsetOfVariables);
|
|
SumOfVariances = zeros(NumberOfVariables,nSteps);
|
|
for h = 1:length(Steps)
|
|
SumOfVariances(:,h) = sum(ConditionalVariance(:,h,:),3);
|
|
end
|
|
|
|
ConditionalVarianceDecomposition = zeros(NumberOfVariables,length(Steps),number_of_state_innovations);
|
|
for i=1:number_of_state_innovations
|
|
for h = 1:length(Steps)
|
|
ConditionalVarianceDecomposition(:,h,i) = squeeze(ConditionalVariance(:,h,i))./SumOfVariances(:,h);
|
|
end
|
|
end
|
|
|
|
% get intersection of requested variables and observed variables with
|
|
% Measurement error
|
|
|
|
if ~all(diag(StateSpaceModel.measurement_error)==0)
|
|
[observable_pos,index_subset,index_observables]=intersect(SubsetOfVariables,StateSpaceModel.observable_pos,'stable');
|
|
ME_Variance=diag(StateSpaceModel.measurement_error);
|
|
|
|
ConditionalVarianceDecomposition_ME = zeros(length(observable_pos),length(Steps),number_of_state_innovations+1);
|
|
for i=1:number_of_state_innovations
|
|
for h = 1:length(Steps)
|
|
ConditionalVarianceDecomposition_ME(:,h,i) = squeeze(ConditionalVariance(index_subset,h,i))./(SumOfVariances(index_subset,h)+ME_Variance(index_observables));
|
|
end
|
|
end
|
|
ConditionalVarianceDecomposition_ME(:,:,number_of_state_innovations+1)=1-sum(ConditionalVarianceDecomposition_ME(:,:,1:number_of_state_innovations),3);
|
|
else
|
|
ConditionalVarianceDecomposition_ME=[];
|
|
end
|