73 lines
3.1 KiB
Matlab
73 lines
3.1 KiB
Matlab
function PackedConditionalVarianceDecomposition = conditional_variance_decomposition(StateSpaceModel, Steps, SubsetOfVariables,sigma_e_is_diagonal)
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% This function computes the conditional variance decomposition of a given state space model
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% for a subset of endogenous variables.
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%
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% INPUTS
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% StateSpaceModel [structure] Specification of the state space model.
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% Steps [integer] 1*h vector of dates.
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% SubsetOfVariables [integer] 1*q vector of indices.
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%
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% OUTPUTS
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% PackedConditionalVarianceDecomposition [double] n(n+1)/2*p matrix, where p is the number of state innovations and
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% n is equal to length(SubsetOfVariables).
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%
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% SPECIAL REQUIREMENTS
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%
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% [1] In this version, absence of measurement errors is assumed...
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% Copyright (C) 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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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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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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number_of_state_innovations = ...
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StateSpaceModel.number_of_state_innovations;
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transition_matrix = StateSpaceModel.transition_matrix;
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number_of_state_equations = ...
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StateSpaceModel.number_of_state_equations;
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nSteps = length(Steps);
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ConditionalVariance = zeros(number_of_state_equations,number_of_state_equations);
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ConditionalVariance = repmat(ConditionalVariance,[1 1 nSteps ...
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number_of_state_innovations]);
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if StateSpaceModel.sigma_e_is_diagonal
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B = StateSpaceModel.impulse_matrix.* ...
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repmat(sqrt(diag(StateSpaceModel.state_innovations_covariance_matrix)'),...
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number_of_state_equations,1);
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else
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B = StateSpaceModel.impulse_matrix*chol(StateSpaceModel.state_innovations_covariance_matrix)';
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end
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for i=1:number_of_state_innovations
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BB = B(:,i)*B(:,i)';
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V = zeros(number_of_state_equations,number_of_state_equations);
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m = 1;
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for h = 1:max(Steps)
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V = transition_matrix*V*transition_matrix'+BB;
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if h == Steps(m)
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ConditionalVariance(:,:,m,i) = V;
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m = m+1;
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end
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end
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end
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ConditionalVariance = ConditionalVariance(SubsetOfVariables,SubsetOfVariables,:,:);
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NumberOfVariables = length(SubsetOfVariables);
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PackedConditionalVarianceDecomposition = zeros(NumberOfVariables*(NumberOfVariables+1)/2,length(Steps),StateSpaceModel.number_of_state_innovations);
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for i=1:number_of_state_innovations
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for h = 1:length(Steps)
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PackedConditionalVarianceDecomposition(:,h,i) = vech(ConditionalVariance(:,:,h,i));
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end
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end |