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DynareMain1.cc

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  • auxiliary_initialization.m 4.80 KiB
    function initial_distribution = auxiliary_initialization(ReducedForm,Y,start,DynareOptions)
    % Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
    %
    % INPUTS
    %    ReducedForm     [structure] Matlab's structure describing the reduced form model.
    %                                       ReducedForm.measurement.H   [double]   (pp x pp) variance matrix of measurement errors.
    %                                       ReducedForm.state.Q         [double]   (qq x qq) variance matrix of state errors.
    %                                       ReducedForm.state.dr        [structure] output of resol.m.
    %    Y                      [double]    pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
    %    start                  [integer]   scalar, likelihood evaluation starts at 'start'.
    %    mf                     [integer]   pp*1 vector of indices.
    %    number_of_particles    [integer]   scalar.
    %
    % OUTPUTS
    %    LIK        [double]    scalar, likelihood
    %    lik        [double]    vector, density of observations in each period.
    %
    % REFERENCES
    %
    % NOTES
    %   The vector "lik" is used to evaluate the jacobian of the likelihood.
    
    % Copyright (C) 2013 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/>.
    persistent init_flag mf0 mf1 number_of_particles
    persistent number_of_observed_variables number_of_structural_innovations
    
    % Set default
    if isempty(start)
        start = 1;
    end
    
    % Set flag for prunning
    %pruning = DynareOptions.particle.pruning;
    
    % Get steady state and mean.
    %steadystate = ReducedForm.steadystate;
    constant = ReducedForm.constant;
    state_variables_steady_state = ReducedForm.state_variables_steady_state;
    
    % Set persistent variables.
    if isempty(init_flag)
        mf0 = ReducedForm.mf0;
        mf1 = ReducedForm.mf1;
        number_of_observed_variables = length(mf1);
        number_of_structural_innovations = length(ReducedForm.Q);
        number_of_particles = DynareOptions.particle.number_of_particles;
        init_flag = 1;
    end
    
    % Set local state space model (first order approximation).
    ghx  = ReducedForm.ghx;
    ghu  = ReducedForm.ghu;
    % Set local state space model (second order approximation).
    ghxx = ReducedForm.ghxx;
    ghuu = ReducedForm.ghuu;
    ghxu = ReducedForm.ghxu;
    
    % Get covariance matrices
    Q = ReducedForm.Q;
    H = ReducedForm.H;
    if isempty(H)
        H = 0;
    end
    
    % Get initial condition for the state vector.
    StateVectorMean = ReducedForm.StateVectorMean;
    StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
    state_variance_rank = size(StateVectorVarianceSquareRoot,2);
    %Q_lower_triangular_cholesky = chol(Q)';
    %if pruning
    %    StateVectorMean_ = StateVectorMean;
    %    StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
    %end
    
    % Set seed for randn().
    set_dynare_seed('default');
    
    % Initialization of the likelihood.
    const_lik = log(2*pi)*number_of_observed_variables;
    
    % Initialization of the weights across particles.
    weights = ones(1,number_of_particles)/number_of_particles ;
    StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
    %if pruning
    %    StateVectors_ = StateVectors;
    %end
    yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
    %if pruning
    %    yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
    %    [tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
    %else
        tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
    %end
    PredictedObservedMean = weights*(tmp(mf1,:)');
    PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
    dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean');
    PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' + H;
    wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
    tau_tilde = weights.*wtilde ;
    tau_tilde = tau_tilde/sum(tau_tilde);
    initial_distribution = resample(StateVectors',tau_tilde',DynareOptions)' ;