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function ConditionalVarianceDecomposition = 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.
%
% 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
% SPECIAL REQUIREMENTS
%
% [1] In this version, absence of measurement errors is assumed...
% Copyright (C) 2010-2017 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
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