2017-09-09 08:42:08 +02:00
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function [ConditionalVarianceDecomposition, ConditionalVarianceDecomposition_ME]= conditional_variance_decomposition(StateSpaceModel, Steps, SubsetOfVariables,sigma_e_is_diagonal)
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2009-06-03 16:50:02 +02:00
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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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2017-05-16 15:10:20 +02:00
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%
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% INPUTS
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2009-06-03 16:50:02 +02:00
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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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2017-09-09 08:42:08 +02:00
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% SubsetOfVariables [integer] 1*q vector of indices (declaration order).
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2017-05-16 15:10:20 +02:00
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%
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% OUTPUTS
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% ConditionalVarianceDecomposition [double] [n h p] array, where
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2010-11-28 11:03:40 +01:00
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% n is equal to length(SubsetOfVariables)
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% h is the number of Steps
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% p is the number of state innovations and
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2017-09-09 08:42:08 +02:00
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% ConditionalVarianceDecomposition_ME [double] [m h p] array, where
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% m is equal to length(intersect(SubsetOfVariables,varobs))
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% h is the number of Steps
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% p is the number of state innovations and
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2009-06-03 16:50:02 +02:00
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2017-05-18 18:36:38 +02:00
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% Copyright (C) 2010-2017 Dynare Team
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2009-06-03 16:50:02 +02:00
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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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2010-01-23 17:55:28 +01:00
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2011-11-20 15:13:05 +01:00
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if any(Steps <= 0)
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error(['Conditional variance decomposition: All periods must be strictly ' ...
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'positive'])
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end
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2009-12-16 18:17:34 +01:00
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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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2010-11-28 11:03:40 +01:00
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order_var = StateSpaceModel.order_var;
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2009-12-16 18:17:34 +01:00
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nSteps = length(Steps);
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2009-10-29 18:16:10 +01:00
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2010-11-28 11:03:40 +01:00
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ConditionalVariance = zeros(number_of_state_equations,nSteps,number_of_state_innovations);
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2009-12-16 18:17:34 +01:00
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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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2010-11-28 11:03:40 +01:00
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ConditionalVariance(order_var,m,i) = diag(V);
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2009-12-16 18:17:34 +01:00
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m = m+1;
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2009-06-03 16:50:02 +02:00
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end
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end
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2009-12-16 18:17:34 +01:00
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end
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2010-11-28 11:03:40 +01:00
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ConditionalVariance = ConditionalVariance(SubsetOfVariables,:,:);
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2009-12-16 18:17:34 +01:00
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NumberOfVariables = length(SubsetOfVariables);
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2010-11-28 11:03:40 +01:00
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SumOfVariances = zeros(NumberOfVariables,nSteps);
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for h = 1:length(Steps)
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SumOfVariances(:,h) = sum(ConditionalVariance(:,h,:),3);
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end
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2017-05-16 15:10:20 +02:00
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ConditionalVarianceDecomposition = zeros(NumberOfVariables,length(Steps),number_of_state_innovations);
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2009-12-16 18:17:34 +01:00
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for i=1:number_of_state_innovations
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for h = 1:length(Steps)
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2010-11-28 11:03:40 +01:00
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ConditionalVarianceDecomposition(:,h,i) = squeeze(ConditionalVariance(:,h,i))./SumOfVariances(:,h);
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2009-12-16 18:17:34 +01:00
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end
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2017-09-09 08:42:08 +02:00
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end
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% get intersection of requested variables and observed variables with
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% Measurement error
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if ~all(StateSpaceModel.measurement_error==0)
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2019-03-26 18:33:15 +01:00
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if isoctave || matlab_ver_less_than('8.1')
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2019-02-15 16:31:24 +01:00
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[observable_pos,index_subset,index_observables]=intersect_stable(SubsetOfVariables,StateSpaceModel.observable_pos);
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else
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[observable_pos,index_subset,index_observables]=intersect(SubsetOfVariables,StateSpaceModel.observable_pos,'stable');
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end
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2017-09-09 08:42:08 +02:00
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ME_Variance=diag(StateSpaceModel.measurement_error);
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ConditionalVarianceDecomposition_ME = zeros(length(observable_pos),length(Steps),number_of_state_innovations+1);
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for i=1:number_of_state_innovations
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for h = 1:length(Steps)
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ConditionalVarianceDecomposition_ME(:,h,i) = squeeze(ConditionalVariance(index_subset,h,i))./(SumOfVariances(index_subset,h)+ME_Variance(index_observables));
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end
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end
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ConditionalVarianceDecomposition_ME(:,:,number_of_state_innovations+1)=1-sum(ConditionalVarianceDecomposition_ME(:,:,1:number_of_state_innovations),3);
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else
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ConditionalVarianceDecomposition_ME=[];
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2019-03-26 18:33:15 +01:00
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end
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