913 lines
36 KiB
Matlab
913 lines
36 KiB
Matlab
function [fval,info,exit_flag,DLIK,Hess,SteadyState,trend_coeff,M_,options_,bayestopt_,dr] = dsge_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,dr, endo_steady_state, exo_steady_state, exo_det_steady_state,derivatives_info)
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% [fval,info,exit_flag,DLIK,Hess,SteadyState,trend_coeff,M_,options_,bayestopt_,oo_] = dsge_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,oo_,derivatives_info)
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% Evaluates the posterior kernel of a DSGE model using the specified
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% kalman_algo; the resulting posterior includes the 2*pi constant of the
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% likelihood function
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%
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% INPUTS
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% - xparam1 [double] current values for the estimated parameters.
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% - dataset_ [structure] dataset after transformations
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% - dataset_info [structure] storing informations about the
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% sample; not used but required for interface
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% - options_ [structure] Matlab's structure describing the current options
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% - M_ [structure] Matlab's structure describing the model
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% - estim_params_ [structure] characterizing parameters to be estimated
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% - bayestopt_ [structure] describing the priors
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% - BoundsInfo [structure] containing prior bounds
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% - dr [structure] Reduced form model.
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% - endo_steady_state [vector] steady state value for endogenous variables
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% - exo_steady_state [vector] steady state value for exogenous variables
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% - exo_det_steady_state [vector] steady state value for exogenous deterministic variables
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% - derivatives_info [structure] derivative info for identification
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%
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% OUTPUTS
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% - fval [double] scalar, value of the likelihood or posterior kernel.
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% - info [integer] 4×1 vector, informations resolution of the model and evaluation of the likelihood.
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% - exit_flag [integer] scalar, equal to 1 (no issues when evaluating the likelihood) or 0 (not able to evaluate the likelihood).
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% - DLIK [double] Vector with score of the likelihood
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% - Hess [double] asymptotic hessian matrix.
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% - SteadyState [double] steady state level for the endogenous variables
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% - trend_coeff [double] Matrix of doubles, coefficients of the deterministic trend in the measurement equation.
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% - M_ [struct] Updated M_ structure described in INPUTS section.
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% - options_ [struct] Updated options_ structure described in INPUTS section.
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% - bayestopt_ [struct] See INPUTS section.
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% - dr [structure] Reduced form model.
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%
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% This function is called by: dynare_estimation_1, mode_check
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% This function calls: dynare_resolve, lyapunov_symm, lyapunov_solver, compute_Pinf_Pstar, kalman_filter_d, missing_observations_kalman_filter_d,
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% univariate_kalman_filter_d, kalman_steady_state, get_perturbation_params_deriv, kalman_filter, missing_observations_kalman_filter, univariate_kalman_filter, priordens
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% Copyright © 2004-2023 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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% Initial author: stephane DOT adjemian AT univ DASH lemans DOT FR
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% Initialization of the returned variables and others...
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fval = [];
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SteadyState = [];
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trend_coeff = [];
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exit_flag = 1;
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info = zeros(4,1);
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if options_.analytic_derivation
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DLIK = NaN(1,length(xparam1));
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else
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DLIK = [];
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end
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Hess = [];
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% Ensure that xparam1 is a column vector.
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% (Don't do the transformation if xparam1 is empty, otherwise it would become a
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% 0×1 matrix, which create issues with older MATLABs when comparing with [] in
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% check_bounds_and_definiteness_estimation)
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if ~isempty(xparam1)
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xparam1 = xparam1(:);
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end
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% Set flag related to analytical derivatives.
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analytic_derivation = options_.analytic_derivation;
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if analytic_derivation
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if options_.loglinear
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error('The analytic_derivation and loglinear options are not compatible')
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end
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if options_.endogenous_prior
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error('The analytic_derivation and endogenous_prior options are not compatible')
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end
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end
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if nargout==1
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analytic_derivation=0;
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end
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if analytic_derivation
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kron_flag=options_.analytic_derivation_mode;
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end
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%------------------------------------------------------------------------------
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% 1. Get the structural parameters & define penalties
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%------------------------------------------------------------------------------
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M_ = set_all_parameters(xparam1,estim_params_,M_);
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[fval,info,exit_flag,Q,H]=check_bounds_and_definiteness_estimation(xparam1, M_, estim_params_, BoundsInfo);
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if info(1)
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return
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end
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%------------------------------------------------------------------------------
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% 2. call model setup & reduction program
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%------------------------------------------------------------------------------
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is_restrict_state_space = true;
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if options_.occbin.likelihood.status
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occbin_options = set_occbin_options(options_);
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if occbin_options.opts_simul.restrict_state_space
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[T,R,SteadyState,info,dr, M_.params,TTx,RRx,CCx, T0, R0] = ...
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occbin.dynare_resolve(M_,options_,dr, endo_steady_state, exo_steady_state, exo_det_steady_state,[],'restrict');
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else
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is_restrict_state_space = false;
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oldoo.restrict_var_list = dr.restrict_var_list;
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oldoo.restrict_columns = dr.restrict_columns;
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dr.restrict_var_list = bayestopt_.smoother_var_list;
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dr.restrict_columns = bayestopt_.smoother_restrict_columns;
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% Linearize the model around the deterministic steady state and extract the matrices of the state equation (T and R).
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[T,R,SteadyState,info,M_,dr, M_.params,TTx,RRx,CCx, T0, R0] = ...
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occbin.dynare_resolve(M_,options_,dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
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dr.restrict_var_list = oldoo.restrict_var_list;
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dr.restrict_columns = oldoo.restrict_columns;
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end
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occbin_.status = true;
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occbin_.info= {options_, dr,endo_steady_state,exo_steady_state,exo_det_steady_state, M_, occbin_options, TTx, RRx, CCx,T0,R0};
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else
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% Linearize the model around the deterministic steady state and extract the matrices of the state equation (T and R).
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[T,R,SteadyState,info,dr, M_.params] = dynare_resolve(M_,options_,dr, endo_steady_state, exo_steady_state, exo_det_steady_state,'restrict');
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occbin_.status = false;
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end
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% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
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if info(1)
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if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
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info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
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info(1) == 81 || info(1) == 84 || info(1) == 85 || info(1) == 86 || ...
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info(1) == 401 || info(1) == 402 || info(1) == 403 || ... %cycle reduction
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info(1) == 411 || info(1) == 412 || info(1) == 413 % logarithmic reduction
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%meaningful second entry of output that can be used
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fval = Inf;
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if isnan(info(2))
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info(4) = 0.1;
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else
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info(4) = info(2);
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end
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exit_flag = 0;
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if analytic_derivation
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DLIK=ones(length(xparam1),1);
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end
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return
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else
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fval = Inf;
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info(4) = 0.1;
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exit_flag = 0;
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if analytic_derivation
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DLIK=ones(length(xparam1),1);
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end
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return
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end
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end
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% check endogenous prior restrictions
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info=endogenous_prior_restrictions(T,R,M_,options_,dr,endo_steady_state,exo_steady_state,exo_det_steady_state);
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if info(1)
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fval = Inf;
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info(4)=info(2);
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exit_flag = 0;
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if analytic_derivation
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DLIK=ones(length(xparam1),1);
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end
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return
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end
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if is_restrict_state_space
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%% Define a vector of indices for the observed variables. Is this really usefull?...
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bayestopt_.mf = bayestopt_.mf1;
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else
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%get location of observed variables and requested smoothed variables in
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%decision rules
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bayestopt_.mf = bayestopt_.smoother_var_list(bayestopt_.smoother_mf);
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end
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% Define the constant vector of the measurement equation.
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if options_.noconstant
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constant = zeros(dataset_.vobs,1);
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else
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if options_.loglinear
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constant = log(SteadyState(bayestopt_.mfys));
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else
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constant = SteadyState(bayestopt_.mfys);
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end
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end
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% Define the deterministic linear trend of the measurement equation.
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if bayestopt_.with_trend
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[trend_addition, trend_coeff]=compute_trend_coefficients(M_,options_,dataset_.vobs,dataset_.nobs);
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trend = repmat(constant,1,dataset_.nobs)+trend_addition;
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else
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trend_coeff = zeros(dataset_.vobs,1);
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trend = repmat(constant,1,dataset_.nobs);
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end
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% Get needed informations for kalman filter routines.
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start = options_.presample+1;
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Z = bayestopt_.mf; %selector for observed variables
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no_missing_data_flag = ~dataset_info.missing.state;
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mm = length(T); %number of states
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pp = dataset_.vobs; %number of observables
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rr = length(Q); %number of shocks
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kalman_tol = options_.kalman_tol;
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diffuse_kalman_tol = options_.diffuse_kalman_tol;
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riccati_tol = options_.riccati_tol;
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Y = transpose(dataset_.data)-trend;
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smpl = size(Y,2);
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%------------------------------------------------------------------------------
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% 3. Initial condition of the Kalman filter
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%------------------------------------------------------------------------------
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kalman_algo = options_.kalman_algo;
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diffuse_periods = 0;
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expanded_state_vector_for_univariate_filter=0;
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singular_diffuse_filter = 0;
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if options_.heteroskedastic_filter
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Qvec=get_Qvec_heteroskedastic_filter(Q,smpl,M_);
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end
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switch options_.lik_init
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case 1% Standard initialization with the steady state of the state equation.
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if kalman_algo~=2
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% Use standard kalman filter except if the univariate filter is explicitely choosen.
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kalman_algo = 1;
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end
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Pstar=lyapunov_solver(T,R,Q,options_);
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Pinf = [];
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a = zeros(mm,1);
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a=set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
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a_0_given_tm1=T*a; %set state prediction for first Kalman step;
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if options_.occbin.likelihood.status
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Z =zeros(length(bayestopt_.mf),size(T,1));
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for i = 1:length(bayestopt_.mf)
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Z(i,bayestopt_.mf(i))=1;
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end
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Zflag = 1;
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else
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Zflag = 0;
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end
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case 2% Initialization with large numbers on the diagonal of the covariance matrix if the states (for non stationary models).
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if kalman_algo ~= 2
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% Use standard kalman filter except if the univariate filter is explicitely choosen.
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kalman_algo = 1;
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end
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Pstar = options_.Harvey_scale_factor*eye(mm);
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Pinf = [];
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a = zeros(mm,1);
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a = set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
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a_0_given_tm1 = T*a; %set state prediction for first Kalman step;
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if options_.occbin.likelihood.status
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Z =zeros(length(bayestopt_.mf),size(T,1));
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for i = 1:length(bayestopt_.mf)
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Z(i,bayestopt_.mf(i))=1;
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end
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Zflag = 1;
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else
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Zflag = 0;
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end
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case 3% Diffuse Kalman filter (Durbin and Koopman)
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% Use standard kalman filter except if the univariate filter is explicitely choosen.
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if kalman_algo == 0
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kalman_algo = 3;
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elseif ~((kalman_algo == 3) || (kalman_algo == 4))
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error(['The model requires Diffuse filter, but you specified a different Kalman filter. You must set options_.kalman_algo ' ...
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'to 0 (default), 3 or 4'])
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end
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[Pstar,Pinf] = compute_Pinf_Pstar(Z,T,R,Q,options_.qz_criterium);
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Z =zeros(length(bayestopt_.mf),size(T,1));
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for i = 1:length(bayestopt_.mf)
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Z(i,bayestopt_.mf(i))=1;
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end
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Zflag = 1;
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if options_.heteroskedastic_filter
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QQ=Qvec;
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else
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QQ=Q;
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end
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% Run diffuse kalman filter on first periods.
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if (kalman_algo==3)
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% Multivariate Diffuse Kalman Filter
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a = zeros(mm,1);
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a = set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
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a_0_given_tm1 = T*a; %set state prediction for first Kalman step;
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Pstar0 = Pstar; % store Pstar
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if no_missing_data_flag
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[dLIK,dlik,a_0_given_tm1,Pstar] = kalman_filter_d(Y, 1, size(Y,2), ...
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a_0_given_tm1, Pinf, Pstar, ...
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kalman_tol, diffuse_kalman_tol, riccati_tol, options_.presample, ...
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T,R,QQ,H,Z,mm,pp,rr);
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else
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[dLIK,dlik,a_0_given_tm1,Pstar] = missing_observations_kalman_filter_d(dataset_info.missing.aindex,dataset_info.missing.number_of_observations,dataset_info.missing.no_more_missing_observations, ...
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Y, 1, size(Y,2), ...
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a_0_given_tm1, Pinf, Pstar, ...
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kalman_tol, diffuse_kalman_tol, riccati_tol, options_.presample, ...
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T,R,QQ,H,Z,mm,pp,rr);
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end
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diffuse_periods = length(dlik);
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if isinf(dLIK)
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% Go to univariate diffuse filter if singularity problem.
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singular_diffuse_filter = 1;
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Pstar = Pstar0;
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end
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end
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if singular_diffuse_filter || (kalman_algo==4)
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% Univariate Diffuse Kalman Filter
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if isequal(H,0)
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H1 = zeros(pp,1);
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mmm = mm;
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else
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if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
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H1 = diag(H);
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mmm = mm;
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else
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%Augment state vector (follows Section 6.4.3 of DK (2012))
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expanded_state_vector_for_univariate_filter=1;
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if Zflag
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Z1=Z;
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else
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Z1=zeros(pp,size(T,2));
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for jz=1:length(Z)
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Z1(jz,Z(jz))=1;
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end
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end
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Z = [Z1, eye(pp)];
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Zflag=1;
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T = blkdiag(T,zeros(pp));
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Q = blkdiag(Q,H);
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R = blkdiag(R,eye(pp));
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Pstar = blkdiag(Pstar,H);
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Pinf = blkdiag(Pinf,zeros(pp));
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H1 = zeros(pp,1);
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mmm = mm+pp;
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if options_.heteroskedastic_filter
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clear QQ
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for kv=1:size(Qvec,3)
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QQ(:,:,kv) = blkdiag(Qvec(:,:,kv),H);
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end
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Qvec=QQ;
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else
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QQ = Q;
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end
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end
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end
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a = zeros(mmm,1);
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a = set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
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a_0_given_tm1 = T*a;
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[dLIK,dlik,a_0_given_tm1,Pstar] = univariate_kalman_filter_d(dataset_info.missing.aindex,...
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dataset_info.missing.number_of_observations,...
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dataset_info.missing.no_more_missing_observations, ...
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Y, 1, size(Y,2), ...
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a_0_given_tm1, Pinf, Pstar, ...
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kalman_tol, diffuse_kalman_tol, riccati_tol, options_.presample, ...
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T,R,QQ,H1,Z,mmm,pp,rr);
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diffuse_periods = size(dlik,1);
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end
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if isnan(dLIK)
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fval = Inf;
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info(1) = 45;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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case 4% Start from the solution of the Riccati equation.
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if kalman_algo ~= 2
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kalman_algo = 1;
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end
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try
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if isequal(H,0)
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Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))));
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else
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Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))),H);
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end
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catch ME
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disp(ME.message)
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disp(['dsge_likelihood:: I am not able to solve the Riccati equation, so I switch to lik_init=1!']);
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options_.lik_init = 1;
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Pstar=lyapunov_solver(T,R,Q,options_);
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end
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Pinf = [];
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||
a = zeros(mm,1);
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a = set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
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a_0_given_tm1 = T*a;
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||
if options_.occbin.likelihood.status
|
||
Z =zeros(length(bayestopt_.mf),size(T,1));
|
||
for i = 1:length(bayestopt_.mf)
|
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Z(i,bayestopt_.mf(i))=1;
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||
end
|
||
Zflag = 1;
|
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else
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Zflag = 0;
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||
end
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case 5 % Old diffuse Kalman filter only for the non stationary variables
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[eigenvect, eigenv] = eig(T);
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||
eigenv = diag(eigenv);
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nstable = length(find(abs(abs(eigenv)-1) > 1e-7));
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||
unstable = find(abs(abs(eigenv)-1) < 1e-7);
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||
V = eigenvect(:,unstable);
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indx_unstable = find(sum(abs(V),2)>1e-5);
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stable = find(sum(abs(V),2)<1e-5);
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nunit = length(eigenv) - nstable;
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||
Pstar = options_.Harvey_scale_factor*eye(nunit);
|
||
if kalman_algo ~= 2
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||
kalman_algo = 1;
|
||
end
|
||
R_tmp = R(stable, :);
|
||
T_tmp = T(stable,stable);
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||
Pstar_tmp=lyapunov_solver(T_tmp,R_tmp,Q,options_);
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||
Pstar(stable, stable) = Pstar_tmp;
|
||
Pinf = [];
|
||
a = zeros(mm,1);
|
||
a = set_Kalman_starting_values(a,M_,dr,options_,bayestopt_);
|
||
a_0_given_tm1 = T*a;
|
||
if options_.occbin.likelihood.status
|
||
Z =zeros(length(bayestopt_.mf),size(T,1));
|
||
for i = 1:length(bayestopt_.mf)
|
||
Z(i,bayestopt_.mf(i))=1;
|
||
end
|
||
Zflag = 1;
|
||
else
|
||
Zflag = 0;
|
||
end
|
||
otherwise
|
||
error('dsge_likelihood:: Unknown initialization approach for the Kalman filter!')
|
||
end
|
||
|
||
if analytic_derivation
|
||
offset = estim_params_.nvx;
|
||
offset = offset+estim_params_.nvn;
|
||
offset = offset+estim_params_.ncx;
|
||
offset = offset+estim_params_.ncn;
|
||
no_DLIK = 0;
|
||
full_Hess = analytic_derivation==2;
|
||
asy_Hess = analytic_derivation==-2;
|
||
outer_product_gradient = analytic_derivation==-1;
|
||
if asy_Hess
|
||
analytic_derivation=1;
|
||
end
|
||
if outer_product_gradient
|
||
analytic_derivation=1;
|
||
end
|
||
DLIK = [];
|
||
AHess = [];
|
||
iv = dr.restrict_var_list;
|
||
if nargin<13 || isempty(derivatives_info)
|
||
[A,B,nou,nou,dr, M_.params] = dynare_resolve(M_,options_,dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
|
||
if ~isempty(estim_params_.var_exo)
|
||
indexo=estim_params_.var_exo(:,1);
|
||
else
|
||
indexo=[];
|
||
end
|
||
if ~isempty(estim_params_.param_vals)
|
||
indparam=estim_params_.param_vals(:,1);
|
||
else
|
||
indparam=[];
|
||
end
|
||
old_order = options_.order;
|
||
if options_.order > 1%not sure whether this check is necessary
|
||
options_.order = 1; fprintf('Reset order to 1 for analytical parameter derivatives.\n');
|
||
end
|
||
old_analytic_derivation_mode = options_.analytic_derivation_mode;
|
||
options_.analytic_derivation_mode = kron_flag;
|
||
if full_Hess
|
||
DERIVS = identification.get_perturbation_params_derivs(M_, options_, estim_params_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state, indparam, indexo, [], true);
|
||
indD2T = reshape(1:M_.endo_nbr^2, M_.endo_nbr, M_.endo_nbr);
|
||
indD2Om = dyn_unvech(1:M_.endo_nbr*(M_.endo_nbr+1)/2);
|
||
D2T = DERIVS.d2KalmanA(indD2T(iv,iv),:);
|
||
D2Om = DERIVS.d2Om(dyn_vech(indD2Om(iv,iv)),:);
|
||
D2Yss = DERIVS.d2Yss(iv,:,:);
|
||
else
|
||
DERIVS = identification.get_perturbation_params_derivs(M_, options_, estim_params_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state, indparam, indexo, [], false);
|
||
end
|
||
DT = zeros(M_.endo_nbr, M_.endo_nbr, size(DERIVS.dghx,3));
|
||
DT(:,M_.nstatic+(1:M_.nspred),:) = DERIVS.dghx;
|
||
DT = DT(iv,iv,:);
|
||
DOm = DERIVS.dOm(iv,iv,:);
|
||
DYss = DERIVS.dYss(iv,:);
|
||
options_.order = old_order; %make sure order is reset (not sure if necessary)
|
||
options_.analytic_derivation_mode = old_analytic_derivation_mode;%make sure analytic_derivation_mode is reset (not sure if necessary)
|
||
else
|
||
DT = derivatives_info.DT(iv,iv,:);
|
||
DOm = derivatives_info.DOm(iv,iv,:);
|
||
DYss = derivatives_info.DYss(iv,:);
|
||
if isfield(derivatives_info,'full_Hess')
|
||
full_Hess = derivatives_info.full_Hess;
|
||
end
|
||
if full_Hess
|
||
D2T = derivatives_info.D2T;
|
||
D2Om = derivatives_info.D2Om;
|
||
D2Yss = derivatives_info.D2Yss;
|
||
end
|
||
if isfield(derivatives_info,'no_DLIK')
|
||
no_DLIK = derivatives_info.no_DLIK;
|
||
end
|
||
clear('derivatives_info');
|
||
end
|
||
DYss = [zeros(size(DYss,1),offset) DYss];
|
||
DH=zeros([length(H),length(H),length(xparam1)]);
|
||
DQ=zeros([size(Q),length(xparam1)]);
|
||
DP=zeros([size(T),length(xparam1)]);
|
||
if full_Hess
|
||
for j=1:size(D2Yss,1)
|
||
tmp(j,:,:) = blkdiag(zeros(offset,offset), squeeze(D2Yss(j,:,:)));
|
||
end
|
||
D2Yss = tmp;
|
||
D2H=sparse(size(D2Om,1),size(D2Om,2)); %zeros([size(H),length(xparam1),length(xparam1)]);
|
||
D2P=sparse(size(D2Om,1),size(D2Om,2)); %zeros([size(T),length(xparam1),length(xparam1)]);
|
||
jcount=0;
|
||
end
|
||
if options_.lik_init==1
|
||
for i=1:estim_params_.nvx
|
||
k =estim_params_.var_exo(i,1);
|
||
DQ(k,k,i) = 2*sqrt(Q(k,k));
|
||
dum = lyapunov_symm(T,DOm(:,:,i),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],options_.debug);
|
||
% kk = find(abs(dum) < 1e-12);
|
||
% dum(kk) = 0;
|
||
DP(:,:,i)=dum;
|
||
if full_Hess
|
||
for j=1:i
|
||
jcount=jcount+1;
|
||
dum = lyapunov_symm(T,dyn_unvech(D2Om(:,jcount)),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],options_.debug);
|
||
% kk = (abs(dum) < 1e-12);
|
||
% dum(kk) = 0;
|
||
D2P(:,jcount)=dyn_vech(dum);
|
||
% D2P(:,:,j,i)=dum;
|
||
end
|
||
end
|
||
end
|
||
end
|
||
offset = estim_params_.nvx;
|
||
for i=1:estim_params_.nvn
|
||
k = estim_params_.var_endo(i,1);
|
||
DH(k,k,i+offset) = 2*sqrt(H(k,k));
|
||
if full_Hess
|
||
D2H(k,k,i+offset,i+offset) = 2;
|
||
end
|
||
end
|
||
offset = offset + estim_params_.nvn;
|
||
if options_.lik_init==1
|
||
for j=1:estim_params_.np
|
||
dum = lyapunov_symm(T,DT(:,:,j+offset)*Pstar*T'+T*Pstar*DT(:,:,j+offset)'+DOm(:,:,j+offset),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],options_.debug);
|
||
% kk = find(abs(dum) < 1e-12);
|
||
% dum(kk) = 0;
|
||
DP(:,:,j+offset)=dum;
|
||
if full_Hess
|
||
DTj = DT(:,:,j+offset);
|
||
DPj = dum;
|
||
for i=1:j+offset
|
||
jcount=jcount+1;
|
||
DTi = DT(:,:,i);
|
||
DPi = DP(:,:,i);
|
||
D2Tij = reshape(D2T(:,jcount),size(T));
|
||
D2Omij = dyn_unvech(D2Om(:,jcount));
|
||
tmp = D2Tij*Pstar*T' + T*Pstar*D2Tij' + DTi*DPj*T' + DTj*DPi*T' + T*DPj*DTi' + T*DPi*DTj' + DTi*Pstar*DTj' + DTj*Pstar*DTi' + D2Omij;
|
||
dum = lyapunov_symm(T,tmp,options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],options_.debug);
|
||
% dum(abs(dum)<1.e-12) = 0;
|
||
D2P(:,jcount) = dyn_vech(dum);
|
||
% D2P(:,:,j+offset,i) = dum;
|
||
end
|
||
end
|
||
end
|
||
end
|
||
if analytic_derivation==1
|
||
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,asy_Hess};
|
||
else
|
||
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P};
|
||
clear DT DYss DOm DP D2T D2Yss D2Om D2H D2P
|
||
end
|
||
else
|
||
analytic_deriv_info={0};
|
||
end
|
||
|
||
%------------------------------------------------------------------------------
|
||
% 4. Likelihood evaluation
|
||
%------------------------------------------------------------------------------
|
||
if options_.heteroskedastic_filter
|
||
Q=Qvec;
|
||
end
|
||
|
||
singularity_has_been_detected = false;
|
||
% First test multivariate filter if specified; potentially abort and use univariate filter instead
|
||
if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
|
||
if no_missing_data_flag && ~options_.occbin.likelihood.status
|
||
if options_.fast_kalman_filter
|
||
if diffuse_periods
|
||
%kalman_algo==3 requires no diffuse periods (stationary
|
||
%observables) as otherwise FE matrix will not be positive
|
||
%definite
|
||
fval = Inf;
|
||
info(1) = 55;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
[LIK,lik] = kalman_filter_fast(Y,diffuse_periods+1,size(Y,2), ...
|
||
a_0_given_tm1,Pstar, ...
|
||
kalman_tol, riccati_tol, ...
|
||
options_.presample, ...
|
||
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, ...
|
||
analytic_deriv_info{:});
|
||
else
|
||
if options_.kalman_filter_mex
|
||
[LIK,lik] = kalman_filter_mex(Y,a_0_given_tm1,Pstar, ...
|
||
kalman_tol, riccati_tol, ...
|
||
T,Q,R,Z,Zflag,H,diffuse_periods, ...
|
||
options_.presample);
|
||
else
|
||
[LIK,lik] = kalman_filter(Y,diffuse_periods+1,size(Y,2), ...
|
||
a_0_given_tm1,Pstar, ...
|
||
kalman_tol, riccati_tol, ...
|
||
options_.rescale_prediction_error_covariance, ...
|
||
options_.presample, ...
|
||
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, ...
|
||
analytic_deriv_info{:});
|
||
end
|
||
end
|
||
else
|
||
[LIK,lik] = missing_observations_kalman_filter(dataset_info.missing.aindex,dataset_info.missing.number_of_observations,dataset_info.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
|
||
a_0_given_tm1, Pstar, ...
|
||
kalman_tol, options_.riccati_tol, ...
|
||
options_.rescale_prediction_error_covariance, ...
|
||
options_.presample, ...
|
||
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, occbin_);
|
||
if occbin_.status && isinf(LIK)
|
||
fval = Inf;
|
||
info(1) = 320;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
end
|
||
if analytic_derivation
|
||
LIK1=LIK;
|
||
LIK=LIK1{1};
|
||
lik1=lik;
|
||
lik=lik1{1};
|
||
end
|
||
if isinf(LIK)
|
||
if options_.use_univariate_filters_if_singularity_is_detected
|
||
singularity_has_been_detected = true;
|
||
if kalman_algo == 1
|
||
kalman_algo = 2;
|
||
else
|
||
kalman_algo = 4;
|
||
end
|
||
else
|
||
fval = Inf;
|
||
info(1) = 50;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
else
|
||
if options_.lik_init==3
|
||
LIK = LIK + dLIK;
|
||
if analytic_derivation==0 && nargout>3
|
||
if ~singular_diffuse_filter
|
||
lik = [dlik; lik];
|
||
else
|
||
lik = [sum(dlik,2); lik];
|
||
end
|
||
end
|
||
end
|
||
end
|
||
end
|
||
|
||
if (kalman_algo==2) || (kalman_algo==4)
|
||
% Univariate Kalman Filter
|
||
% resetting measurement error covariance matrix when necessary following DK (2012), Section 6.4.3 %
|
||
if isequal(H,0)
|
||
H1 = zeros(pp,1);
|
||
mmm = mm;
|
||
if analytic_derivation
|
||
DH = zeros(pp,length(xparam1));
|
||
end
|
||
else
|
||
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
||
H1 = diag(H);
|
||
mmm = mm;
|
||
clear('tmp')
|
||
if analytic_derivation
|
||
for j=1:pp
|
||
tmp(j,:)=DH(j,j,:);
|
||
end
|
||
DH=tmp;
|
||
end
|
||
else
|
||
if ~expanded_state_vector_for_univariate_filter
|
||
Z1=zeros(pp,size(T,2));
|
||
for jz=1:length(Z)
|
||
Z1(jz,Z(jz))=1;
|
||
end
|
||
Z = [Z1, eye(pp)];
|
||
Zflag=1;
|
||
T = blkdiag(T,zeros(pp));
|
||
if options_.heteroskedastic_filter
|
||
clear Q
|
||
for kv=1:size(Qvec,3)
|
||
Q(:,:,kv) = blkdiag(Qvec(:,:,kv),H);
|
||
end
|
||
else
|
||
Q = blkdiag(Q,H);
|
||
end
|
||
R = blkdiag(R,eye(pp));
|
||
Pstar = blkdiag(Pstar,H);
|
||
Pinf = blkdiag(Pinf,zeros(pp));
|
||
H1 = zeros(pp,1);
|
||
Zflag=1;
|
||
end
|
||
mmm = mm+pp;
|
||
if singularity_has_been_detected
|
||
a_tmp = zeros(mmm,1);
|
||
a_tmp(1:length(a_0_given_tm1)) = a_0_given_tm1;
|
||
a_0_given_tm1 = a_tmp;
|
||
elseif ~expanded_state_vector_for_univariate_filter
|
||
a_0_given_tm1 = [a_0_given_tm1; zeros(pp,1)];
|
||
end
|
||
end
|
||
end
|
||
if analytic_derivation
|
||
analytic_deriv_info{5}=DH;
|
||
end
|
||
[LIK, lik] = univariate_kalman_filter(dataset_info.missing.aindex,dataset_info.missing.number_of_observations,dataset_info.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
|
||
a_0_given_tm1,Pstar, ...
|
||
options_.kalman_tol, ...
|
||
options_.riccati_tol, ...
|
||
options_.presample, ...
|
||
T,Q,R,H1,Z,mmm,pp,rr,Zflag,diffuse_periods,analytic_deriv_info{:});
|
||
if analytic_derivation
|
||
LIK1=LIK;
|
||
LIK=LIK1{1};
|
||
lik1=lik;
|
||
lik=lik1{1};
|
||
end
|
||
if options_.lik_init==3
|
||
LIK = LIK+dLIK;
|
||
if analytic_derivation==0 && nargout>3
|
||
lik = [dlik; lik];
|
||
end
|
||
end
|
||
end
|
||
|
||
if analytic_derivation
|
||
if no_DLIK==0
|
||
DLIK = LIK1{2};
|
||
end
|
||
if full_Hess
|
||
Hess = -LIK1{3};
|
||
end
|
||
if asy_Hess
|
||
Hess = LIK1{3};
|
||
end
|
||
end
|
||
|
||
if isnan(LIK)
|
||
fval = Inf;
|
||
info(1) = 45;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if imag(LIK)~=0
|
||
fval = Inf;
|
||
info(1) = 46;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if isinf(LIK)~=0
|
||
fval = Inf;
|
||
info(1) = 50;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
likelihood = LIK;
|
||
|
||
% ------------------------------------------------------------------------------
|
||
% 5. Adds prior if necessary
|
||
% ------------------------------------------------------------------------------
|
||
if analytic_derivation
|
||
if full_Hess
|
||
[lnprior, dlnprior, d2lnprior] = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||
Hess = Hess - d2lnprior;
|
||
else
|
||
[lnprior, dlnprior] = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||
end
|
||
if no_DLIK==0
|
||
DLIK = DLIK - dlnprior';
|
||
end
|
||
if outer_product_gradient
|
||
dlik = lik1{2};
|
||
dlik=[- dlnprior; dlik(start:end,:)];
|
||
Hess = dlik'*dlik;
|
||
end
|
||
else
|
||
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||
end
|
||
|
||
if options_.endogenous_prior==1
|
||
if options_.lik_init==2 || options_.lik_init==3
|
||
error('Endogenous prior not supported with non-stationary models')
|
||
else
|
||
[lnpriormom] = endogenous_prior(Y,dataset_info,Pstar,bayestopt_,H);
|
||
fval = (likelihood-lnprior-lnpriormom);
|
||
end
|
||
else
|
||
fval = (likelihood-lnprior);
|
||
end
|
||
|
||
if options_.prior_restrictions.status
|
||
tmp = feval(options_.prior_restrictions.routine, M_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state, options_, dataset_, dataset_info);
|
||
fval = fval - tmp;
|
||
end
|
||
|
||
if isnan(fval)
|
||
fval = Inf;
|
||
info(1) = 47;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if imag(fval)~=0
|
||
fval = Inf;
|
||
info(1) = 48;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if ~options_.kalman.keep_kalman_algo_if_singularity_is_detected
|
||
% Update options_.kalman_algo.
|
||
options_.kalman_algo = kalman_algo;
|
||
end
|
||
|
||
if analytic_derivation==0 && nargout>3
|
||
lik=lik(start:end,:);
|
||
DLIK=[-lnprior; lik(:)];
|
||
end
|
||
|
||
function a=set_Kalman_starting_values(a,M_,dr,options_,bayestopt_)
|
||
% function a=set_Kalman_starting_values(a,M_,dr,options_,bayestopt_)
|
||
% Sets initial states guess for Kalman filter/smoother based on M_.filter_initial_state
|
||
%
|
||
% INPUTS
|
||
% o a [double] (p*1) vector of states
|
||
% o M_ [structure] decribing the model
|
||
% o dr [structure] storing the decision rules
|
||
% o options_ [structure] describing the options
|
||
% o bayestopt_ [structure] describing the priors
|
||
%
|
||
% OUTPUTS
|
||
% o a [double] (p*1) vector of set initial states
|
||
|
||
if isfield(M_,'filter_initial_state') && ~isempty(M_.filter_initial_state)
|
||
state_indices=dr.order_var(dr.restrict_var_list(bayestopt_.mf0));
|
||
for ii=1:size(state_indices,1)
|
||
if ~isempty(M_.filter_initial_state{state_indices(ii),1})
|
||
if options_.loglinear && ~options_.logged_steady_state
|
||
a(bayestopt_.mf0(ii)) = log(eval(M_.filter_initial_state{state_indices(ii),2})) - log(dr.ys(state_indices(ii)));
|
||
elseif ~options_.loglinear && ~options_.logged_steady_state
|
||
a(bayestopt_.mf0(ii)) = eval(M_.filter_initial_state{state_indices(ii),2}) - dr.ys(state_indices(ii));
|
||
else
|
||
error(['The steady state is logged. This should not happen. Please contact the developers'])
|
||
end
|
||
end
|
||
end
|
||
end
|
||
|
||
function occbin_options = set_occbin_options(options_)
|
||
|
||
% this builds the opts_simul options field needed by occbin.solver
|
||
occbin_options.opts_simul = options_.occbin.simul;
|
||
occbin_options.opts_simul.curb_retrench = options_.occbin.likelihood.curb_retrench;
|
||
occbin_options.opts_simul.maxit = options_.occbin.likelihood.maxit;
|
||
occbin_options.opts_simul.periods = options_.occbin.likelihood.periods;
|
||
occbin_options.opts_simul.check_ahead_periods = options_.occbin.likelihood.check_ahead_periods;
|
||
occbin_options.opts_simul.max_check_ahead_periods = options_.occbin.likelihood.max_check_ahead_periods;
|
||
occbin_options.opts_simul.periodic_solution = options_.occbin.likelihood.periodic_solution;
|
||
occbin_options.opts_simul.restrict_state_space = options_.occbin.likelihood.restrict_state_space;
|
||
|
||
occbin_options.opts_simul.full_output = options_.occbin.likelihood.full_output;
|
||
occbin_options.opts_simul.piecewise_only = options_.occbin.likelihood.piecewise_only;
|
||
if ~isempty(options_.occbin.smoother.init_binding_indicator)
|
||
occbin_options.opts_simul.init_binding_indicator = options_.occbin.likelihood.init_binding_indicator;
|
||
occbin_options.opts_simul.init_regime_history=options_.occbin.likelihood.init_regime_history;
|
||
end
|