78 lines
3.1 KiB
Matlab
78 lines
3.1 KiB
Matlab
function W_opt = optimal_weighting_matrix(m_data, moments, q_lag)
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% W_opt = optimal_weighting_matrix(m_data, moments, q_lag)
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% -------------------------------------------------------------------------
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% This function computes the optimal weigthing matrix by a Bartlett kernel with maximum lag q_lag
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% Adapted from replication codes of Andreasen, Fernández-Villaverde, Rubio-Ramírez (2018):
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% "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications",
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% Review of Economic Studies, 85(1):1-49.
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% -------------------------------------------------------------------------
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% INPUTS
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% o m_data [T x numMom] selected data moments at each point in time
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% o moments [numMom x 1] selected estimated moments (either data_moments or estimated model_moments)
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% o q_lag [integer] Bartlett kernel maximum lag order
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% -------------------------------------------------------------------------
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% OUTPUTS
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% o W_opt [numMom x numMom] optimal weighting matrix
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% -------------------------------------------------------------------------
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% This function is called by
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% o mom.run.m
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% -------------------------------------------------------------------------
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% This function calls:
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% o corr_matrix (embedded)
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% -------------------------------------------------------------------------
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% Copyright © 2020-2023 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 <https://www.gnu.org/licenses/>.
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% initialize
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[T,num_Mom] = size(m_data); % note that in m_data NaN values (due to leads or lags in matched_moments and missing data) were replaced by the mean
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% center around moments (could be either data_moments or model_moments)
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h_func = m_data - repmat(moments',T,1);
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% the required correlation matrices
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gamma_array = zeros(num_Mom,num_Mom,q_lag);
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gamma0 = corr_matrix(h_func,T,num_Mom,0);
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if q_lag > 0
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for ii=1:q_lag
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gamma_array(:,:,ii) = corr_matrix(h_func,T,num_Mom,ii);
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end
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end
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% the estimate of S
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S = gamma0;
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if q_lag > 0
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for ii=1:q_lag
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S = S + (1-ii/(q_lag+1))*(gamma_array(:,:,ii) + gamma_array(:,:,ii)');
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end
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end
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% the estimate of W
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W_opt = S\eye(size(S,1));
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W_opt = (W_opt+W_opt')/2; % ensure symmetry
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end % main function end
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% The correlation matrix
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function gamma_corr = corr_matrix(h_func,T,num_Mom,v)
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gamma_corr = zeros(num_Mom,num_Mom);
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for t = 1+v:T
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gamma_corr = gamma_corr + h_func(t-v,:)'*h_func(t,:);
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end
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gamma_corr = gamma_corr/T;
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end % corr_matrix end |