80 lines
3.2 KiB
Matlab
80 lines
3.2 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
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% o Andreasen, Fernández-Villaverde, Rubio-Ramírez (2018): "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications", 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 CorrMatrix (embedded)
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% =========================================================================
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% Copyright © 2020-2021 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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% -------------------------------------------------------------------------
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% Author(s):
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% o Willi Mutschler (willi@mutschler.eu)
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% o Johannes Pfeifer (jpfeifer@uni-koeln.de)
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% =========================================================================
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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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GAMA_array = zeros(num_Mom,num_Mom,q_lag);
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GAMA0 = 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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GAMA_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 = GAMA0;
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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))*(GAMA_array(:,:,ii) + GAMA_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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end
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% The correlation matrix
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function GAMA_corr = Corr_Matrix(h_Func,T,num_Mom,v)
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GAMA_corr = zeros(num_Mom,num_Mom);
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for t = 1+v:T
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GAMA_corr = GAMA_corr + h_Func(t-v,:)'*h_Func(t,:);
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end
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GAMA_corr = GAMA_corr/T;
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end
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