639 lines
26 KiB
Matlab
639 lines
26 KiB
Matlab
function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp,trend_addition,state_uncertainty,M_,oo_,bayestopt_] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value,M_,oo_,options_,bayestopt_,estim_params_,varargin)
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% Estimation of the smoothed variables and innovations.
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%
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% INPUTS
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% o xparam1 [double] (p*1) vector of (estimated) parameters.
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% o gend [integer] scalar specifying the number of observations ==> varargin{1}.
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% o Y [double] (n*T) matrix of data.
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% o data_index [cell] 1*smpl cell of column vectors of indices.
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% o missing_value 1 if missing values, 0 otherwise
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% o M_ [structure] decribing the model
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% o oo_ [structure] storing the results
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% o options_ [structure] describing the options
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% o bayestopt_ [structure] describing the priors
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% o estim_params_ [structure] characterizing parameters to be estimated
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%
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% OUTPUTS
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% o alphahat [double] (m*T) matrix, smoothed endogenous variables (a_{t|T}) (decision-rule order)
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% o etahat [double] (r*T) matrix, smoothed structural shocks (r>=n is the number of shocks).
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% o epsilonhat [double] (n*T) matrix, smoothed measurement errors.
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% o ahat [double] (m*T) matrix, updated (endogenous) variables (a_{t|t}) (decision-rule order)
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% o SteadyState [double] (m*1) vector specifying the steady state level of each endogenous variable (declaration order)
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% o trend_coeff [double] (n*1) vector, parameters specifying the slope of the trend associated to each observed variable.
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% o aK [double] (K,n,T+K) array, k (k=1,...,K) steps ahead
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% filtered (endogenous) variables (decision-rule order)
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% o T and R [double] Matrices defining the state equation (T is the (m*m) transition matrix).
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% o P: (m*m*(T+1)) 3D array of one-step ahead forecast error variance
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% matrices (decision-rule order)
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% o PK: (K*m*m*(T+K)) 4D array of k-step ahead forecast error variance
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% matrices (meaningless for periods 1:d) (decision-rule order)
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% o decomp (K*m*r*(T+K)) 4D array of shock decomposition of k-step ahead
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% filtered variables (decision-rule order)
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% o trend_addition [double] (n*T) pure trend component; stored in options_.varobs order
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% o state_uncertainty [double] (K,K,T) array, storing the uncertainty
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% about the smoothed state (decision-rule order)
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% o M_ [structure] decribing the model
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% o oo_ [structure] storing the results
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% o bayestopt_ [structure] describing the priors
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%
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% Notes:
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% m: number of endogenous variables (M_.endo_nbr)
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% T: number of Time periods (options_.nobs)
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% r: number of strucural shocks (M_.exo_nbr)
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% n: number of observables (length(options_.varobs))
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% K: maximum forecast horizon (max(options_.nk))
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%
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% To get variables that are stored in decision rule order in order of declaration
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% as in M_.endo_names, ones needs code along the lines of:
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% variables_declaration_order(dr.order_var,:) = alphahat
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%
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% Defines bayestopt_.mf = bayestopt_.smoother_mf (positions of observed variables
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% and requested smoothed variables in decision rules (decision rule order)) and
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% passes it back via global variable
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%
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% ALGORITHM
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% Diffuse Kalman filter (Durbin and Koopman)
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%
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% SPECIAL REQUIREMENTS
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% None
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% Copyright © 2006-2020 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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alphahat = [];
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etahat = [];
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epsilonhat = [];
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ahat = [];
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SteadyState = [];
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trend_coeff = [];
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aK = [];
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T = [];
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R = [];
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P = [];
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PK = [];
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decomp = [];
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vobs = length(options_.varobs);
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smpl = size(Y,2);
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if ~isempty(xparam1) %not calibrated model
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M_ = set_all_parameters(xparam1,estim_params_,M_);
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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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length_varargin=length(varargin);
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if ~options_.smoother_redux
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%store old setting of restricted var_list
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oldoo.restrict_var_list = oo_.dr.restrict_var_list;
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oldoo.restrict_columns = oo_.dr.restrict_columns;
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oo_.dr.restrict_var_list = bayestopt_.smoother_var_list;
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oo_.dr.restrict_columns = bayestopt_.smoother_restrict_columns;
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[T,R,SteadyState,info,M_,oo_] = dynare_resolve(M_,options_,oo_);
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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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else
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if ~options_.occbin.smoother.status
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[T,R,SteadyState,info,M_,oo_] = dynare_resolve(M_,options_,oo_,'restrict');
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else
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[T,R,SteadyState,info,M_,oo_,~,~,~, T0, R0] = ...
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occbin.dynare_resolve(M_,options_,oo_,[],'restrict');
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varargin{length_varargin+1}=T0;
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varargin{length_varargin+2}=R0;
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end
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bayestopt_.mf = bayestopt_.mf1;
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end
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if options_.occbin.smoother.status
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occbin_info.status = true;
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occbin_info.info= [{options_,oo_,M_} varargin];
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else
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occbin_info.status = false;
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end
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if info~=0
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print_info(info,options_.noprint, options_);
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return
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end
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if options_.noconstant
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constant = zeros(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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trend_coeff = zeros(vobs,1);
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if bayestopt_.with_trend == 1
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[trend_addition, trend_coeff] =compute_trend_coefficients(M_,options_,vobs,gend);
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trend = constant*ones(1,gend)+trend_addition;
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else
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trend_addition=zeros(size(constant,1),gend);
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trend = constant*ones(1,gend);
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end
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start = options_.presample+1;
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np = size(T,1);
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mf = bayestopt_.mf;
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% ------------------------------------------------------------------------------
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% 3. Initial condition of the Kalman filter
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% ------------------------------------------------------------------------------
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%
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% Here, Pinf and Pstar are determined. If the model is stationary, determine
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% Pstar as the solution of the Lyapunov equation and set Pinf=[] (Notation follows
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% Koopman/Durbin (2003), Journal of Time Series Analysis 24(1))
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%
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Q = M_.Sigma_e;
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H = M_.H;
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if isequal(H,0)
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H = zeros(vobs,vobs);
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end
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Z = zeros(vobs,size(T,2));
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for i=1:vobs
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Z(i,mf(i)) = 1;
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end
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expanded_state_vector_for_univariate_filter=0;
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kalman_algo = options_.kalman_algo;
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if options_.lik_init == 1 % Kalman filter
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if kalman_algo ~= 2
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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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elseif options_.lik_init == 2 % Old Diffuse Kalman filter
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if kalman_algo ~= 2
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kalman_algo = 1;
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end
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Pstar = options_.Harvey_scale_factor*eye(np);
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Pinf = [];
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elseif options_.lik_init == 3 % Diffuse Kalman filter
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if kalman_algo ~= 4
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kalman_algo = 3;
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else
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if ~all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is not diagonal...
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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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T = blkdiag(T,zeros(vobs));
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np = size(T,1);
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Q = blkdiag(Q,H);
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R = blkdiag(R,eye(vobs));
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H = zeros(vobs,vobs);
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Z = [Z, eye(vobs)];
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end
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end
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[Pstar,Pinf] = compute_Pinf_Pstar(mf,T,R,Q,options_.qz_criterium);
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elseif options_.lik_init == 4 % Start from the solution of the Riccati equation.
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Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(mf,np,vobs)),H);
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Pinf = [];
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if kalman_algo~=2
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kalman_algo = 1;
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end
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elseif options_.lik_init == 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(np);
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if kalman_algo ~= 2
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kalman_algo = 1;
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end
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R_tmp = R(stable, :);
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T_tmp = T(stable,stable);
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Pstar_tmp=lyapunov_solver(T_tmp,R_tmp,Q,DynareOptions);
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Pstar(stable, stable) = Pstar_tmp;
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Pinf = [];
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end
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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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data1 = Y-trend;
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% -----------------------------------------------------------------------------
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% 4. Kalman smoother
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% -----------------------------------------------------------------------------
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if ~missing_value
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for i=1:smpl
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data_index{i}=(1:vobs)';
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end
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end
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ST = T;
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R1 = R;
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if options_.heteroskedastic_filter
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Q=get_Qvec_heteroskedastic_filter(Q,smpl,M_);
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end
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if options_.occbin.smoother.status
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if kalman_algo == 1
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kalman_algo = 2;
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end
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if kalman_algo == 3
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kalman_algo = 4;
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end
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end
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if kalman_algo == 1 || kalman_algo == 3
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a_initial = zeros(np,1);
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a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
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a_initial=T*a_initial; %set state prediction for first Kalman step;
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d] = missing_DiffuseKalmanSmootherH1_Z(a_initial,ST, ...
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Z,R1,Q,H,Pinf,Pstar, ...
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data1,vobs,np,smpl,data_index, ...
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options_.nk,kalman_tol,diffuse_kalman_tol,options_.filter_decomposition,options_.smoothed_state_uncertainty,options_.filter_covariance,options_.smoother_redux);
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if isinf(alphahat)
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if kalman_algo == 1
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fprintf('\nDsgeSmoother: Switching to univariate filter. This may be a sign of stochastic singularity.\n')
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kalman_algo = 2;
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elseif kalman_algo == 3
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fprintf('\nDsgeSmoother: Switching to univariate filter. This is usually due to co-integration in diffuse filter,\n')
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fprintf(' otherwise it may be a sign of stochastic singularity.\n')
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kalman_algo = 4;
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else
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error('This case shouldn''t happen')
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end
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end
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end
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if kalman_algo == 2 || kalman_algo == 4
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if ~all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
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if ~expanded_state_vector_for_univariate_filter
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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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Z = [Z, eye(vobs)];
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ST = blkdiag(ST,zeros(vobs));
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np = size(ST,1);
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if options_.heteroskedastic_filter
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Qvec=Q;
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Q=NaN(size(Qvec,1)+size(H,1),size(Qvec,1)+size(H,1),smpl+1);
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for kv=1:size(Qvec,3)
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Q(:,:,kv) = blkdiag(Qvec(:,:,kv),H);
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end
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else
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Q = blkdiag(Q,H);
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end
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R1 = blkdiag(R,eye(vobs));
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if kalman_algo == 4
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%recompute Schur state space transformation with
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%expanded state space
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[Pstar,Pinf] = compute_Pinf_Pstar(mf,ST,R1,Q,options_.qz_criterium);
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else
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Pstar = blkdiag(Pstar,H);
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if ~isempty(Pinf)
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Pinf = blkdiag(Pinf,zeros(vobs));
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end
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end
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%now reset H to 0
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H = zeros(vobs,vobs);
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else
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%do nothing, state vector was already expanded
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end
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end
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a_initial = zeros(np,1);
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a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
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a_initial=ST*a_initial; %set state prediction for first Kalman step;
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, regimes_,TT,RR,CC] = missing_DiffuseKalmanSmootherH3_Z(a_initial,ST, ...
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Z,R1,Q,diag(H), ...
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Pinf,Pstar,data1,vobs,np,smpl,data_index, ...
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options_.nk,kalman_tol,diffuse_kalman_tol, ...
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options_.filter_decomposition,options_.smoothed_state_uncertainty,options_.filter_covariance,options_.smoother_redux,occbin_info);
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if options_.occbin.smoother.status
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oo_.occbin.smoother.regime_history = regimes_;
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end
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end
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if expanded_state_vector_for_univariate_filter && (kalman_algo == 2 || kalman_algo == 4)
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% extracting measurement errors
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% removing observed variables from the state vector
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k = (1:np-vobs);
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alphahat = alphahat(k,:);
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ahat = ahat(k,:);
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aK = aK(:,k,:,:);
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epsilonhat=etahat(end-vobs+1:end,:);
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etahat=etahat(1:end-vobs,:);
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if ~isempty(PK)
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PK = PK(:,k,k,:);
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end
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if ~isempty(decomp)
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decomp = decomp(:,k,:,:);
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end
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if ~isempty(P)
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P = P(k,k,:);
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end
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if ~isempty(state_uncertainty)
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state_uncertainty = state_uncertainty(k,k,:);
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end
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end
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if ~options_.smoother_redux
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%reset old setting of restricted var_list
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oo_.dr.restrict_var_list = oldoo.restrict_var_list;
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oo_.dr.restrict_columns = oldoo.restrict_columns;
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else
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if options_.block == 0
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ic = [ M_.nstatic+(1:M_.nspred) M_.endo_nbr+(1:size(oo_.dr.ghx,2)-M_.nspred) ]';
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else
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ic = oo_.dr.restrict_columns;
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end
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if options_.occbin.smoother.status
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% reconstruct occbin smoother
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if length_varargin>0
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% sequence of regimes is provided in input
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isoccbin=1;
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else
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isoccbin=0;
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end
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if length_varargin>1
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TT=varargin{2};
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RR=varargin{3};
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CC=varargin{4};
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if size(TT,3)<(smpl+1)
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TT=repmat(T,1,1,smpl+1);
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RR=repmat(R,1,1,smpl+1);
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CC=repmat(zeros(mm,1),1,smpl+1);
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end
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end
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if isoccbin==0
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[A,B] = kalman_transition_matrix(oo_.dr,(1:M_.endo_nbr)',ic,M_.exo_nbr);
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else
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opts_simul = options_.occbin.simul;
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end
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aaa=zeros(M_.endo_nbr,gend);
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aaa(oo_.dr.restrict_var_list,:)=alphahat;
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for k=2:gend
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if isoccbin
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A = TT(:,:,k);
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B = RR(:,:,k);
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C = CC(:,k);
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else
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C=0;
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end
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aaa(:,k) = C+A*aaa(:,k-1)+B*etahat(:,k);
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end
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alphahat=aaa;
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aaa=zeros(M_.endo_nbr,gend);
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bbb=zeros(M_.endo_nbr,gend);
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bbb(oo_.dr.restrict_var_list,:)=ahat;
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aaa(oo_.dr.restrict_var_list,:)=aahat;
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for k=d+2:gend
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if isoccbin
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A = TT(:,:,k);
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B = RR(:,:,k);
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C = CC(:,k);
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bbb(:,k) = C+A*aaa(:,k-1)+B*eehat(:,k);
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else
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opts_simul.curb_retrench = options_.occbin.smoother.curb_retrench;
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opts_simul.waitbar = options_.occbin.smoother.waitbar;
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opts_simul.maxit = options_.occbin.smoother.maxit;
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opts_simul.periods = options_.occbin.smoother.periods;
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opts_simul.check_ahead_periods = options_.occbin.smoother.check_ahead_periods;
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opts_simul.full_output = options_.occbin.smoother.full_output;
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opts_simul.piecewise_only = options_.occbin.smoother.piecewise_only;
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opts_simul.SHOCKS = zeros(options_.nk,M_.exo_nbr);
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opts_simul.SHOCKS(1,:) = eehat(:,k);
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tmp=zeros(M_.endo_nbr,1);
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tmp(oo_.dr.restrict_var_list,1)=aahat(:,k-1);
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opts_simul.endo_init = tmp(oo_.dr.inv_order_var,1);
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opts_simul.init_regime = []; %regimes_(k);
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opts_simul.waitbar=0;
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options_.occbin.simul=opts_simul;
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[~, out] = occbin.solver(M_,oo_,options_);
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|
% regime in out should be identical to regimes_(k-2) moved one
|
|
% period ahead (so if regimestart was [1 5] it should be [1 4]
|
|
% in out
|
|
% end
|
|
bbb(oo_.dr.inv_order_var,k) = out.piecewise(1,:);
|
|
end
|
|
end
|
|
% do not overwrite accurate computations using reduced st. space
|
|
bbb(oo_.dr.restrict_var_list,:)=ahat;
|
|
ahat0=ahat;
|
|
ahat=bbb;
|
|
if ~isempty(P)
|
|
PP=zeros(M_.endo_nbr,M_.endo_nbr,gend+1);
|
|
PP(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=P;
|
|
P=PP;
|
|
clear PP
|
|
end
|
|
|
|
if ~isempty(state_uncertainty)
|
|
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr,gend);
|
|
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=state_uncertainty;
|
|
state_uncertainty=sstate_uncertainty;
|
|
clear sstate_uncertainty
|
|
end
|
|
|
|
aaa = zeros(options_.nk,M_.endo_nbr,gend+options_.nk);
|
|
aaa(:,oo_.dr.restrict_var_list,:)=aK;
|
|
|
|
for k=2:gend+1
|
|
opts_simul.curb_retrench = options_.occbin.smoother.curb_retrench;
|
|
opts_simul.waitbar = options_.occbin.smoother.waitbar;
|
|
opts_simul.maxit = options_.occbin.smoother.maxit;
|
|
opts_simul.periods = options_.occbin.smoother.periods;
|
|
opts_simul.check_ahead_periods = options_.occbin.smoother.check_ahead_periods;
|
|
opts_simul.full_output = options_.occbin.smoother.full_output;
|
|
opts_simul.piecewise_only = options_.occbin.smoother.piecewise_only;
|
|
opts_simul.SHOCKS = zeros(options_.nk,M_.exo_nbr);
|
|
tmp=zeros(M_.endo_nbr,1);
|
|
tmp(oo_.dr.restrict_var_list,1)=ahat0(:,k-1);
|
|
opts_simul.endo_init = tmp(oo_.dr.inv_order_var,1);
|
|
opts_simul.init_regime = []; %regimes_(k);
|
|
opts_simul.waitbar=0;
|
|
options_.occbin.simul=opts_simul;
|
|
[~, out] = occbin.solver(M_,oo_,options_);
|
|
% regime in out should be identical to regimes_(k-2) moved one
|
|
% period ahead (so if regimestart was [1 5] it should be [1 4]
|
|
% in out
|
|
% end
|
|
for jnk=1:options_.nk
|
|
aaa(jnk,oo_.dr.inv_order_var,k+jnk-1) = out.piecewise(jnk,:);
|
|
end
|
|
end
|
|
aK=aaa;
|
|
|
|
if ~isempty(PK)
|
|
PP = zeros(options_.nk,M_.endo_nbr,M_.endo_nbr,gend+options_.nk);
|
|
PP(:,oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:) = PK;
|
|
PK=PP;
|
|
clear PP
|
|
end
|
|
else
|
|
% reconstruct smoother
|
|
[A,B] = kalman_transition_matrix(oo_.dr,(1:M_.endo_nbr)',ic,M_.exo_nbr);
|
|
iT = pinv(T);
|
|
Tstar = A(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),oo_.dr.restrict_var_list);
|
|
Rstar = B(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),:);
|
|
C = Tstar*iT;
|
|
D = Rstar-C*R;
|
|
static_var_list = ~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list);
|
|
ilagged = any(abs(C*T-Tstar)'>1.e-12);
|
|
static_var_list0 = static_var_list;
|
|
static_var_list0(static_var_list) = ilagged;
|
|
static_var_list(static_var_list) = ~ilagged;
|
|
% reconstruct smoothed variables
|
|
aaa=zeros(M_.endo_nbr,gend);
|
|
aaa(oo_.dr.restrict_var_list,:)=alphahat;
|
|
for k=1:gend
|
|
aaa(static_var_list,k) = C(~ilagged,:)*alphahat(:,k)+D(~ilagged,:)*etahat(:,k);
|
|
end
|
|
if any(ilagged)
|
|
for k=2:gend
|
|
aaa(static_var_list0,k) = Tstar(ilagged,:)*alphahat(:,k-1)+Rstar(ilagged,:)*etahat(:,k);
|
|
end
|
|
end
|
|
alphahat=aaa;
|
|
|
|
% reconstruct updated variables
|
|
aaa=zeros(M_.endo_nbr,gend);
|
|
aaa(oo_.dr.restrict_var_list,:)=ahat;
|
|
for k=1:gend
|
|
aaa(static_var_list,k) = C(~ilagged,:)*ahat(:,k)+D(~ilagged,:)*eehat(:,k);
|
|
end
|
|
if any(ilagged)
|
|
% bbb=zeros(M_.endo_nbr,gend);
|
|
% bbb(oo_.dr.restrict_var_list,:)=aahat;
|
|
for k=d+2:gend
|
|
aaa(static_var_list0,k) = Tstar(ilagged,:)*aahat(:,k-1)+Rstar(ilagged,:)*eehat(:,k);
|
|
end
|
|
end
|
|
ahat1=aaa;
|
|
% reconstruct aK
|
|
if isempty(options_.nk)
|
|
options_.nk=1;
|
|
end
|
|
aaa = zeros(options_.nk,M_.endo_nbr,gend+options_.nk);
|
|
aaa(:,oo_.dr.restrict_var_list,:)=aK;
|
|
for k=1:gend
|
|
for jnk=1:options_.nk
|
|
aaa(jnk,static_var_list,k+jnk) = C(~ilagged,:)*dynare_squeeze(aK(jnk,:,k+jnk));
|
|
end
|
|
end
|
|
if any(ilagged)
|
|
for k=1:gend
|
|
aaa(1,static_var_list0,k+1) = Tstar(ilagged,:)*ahat(:,k);
|
|
for jnk=2:options_.nk
|
|
aaa(jnk,static_var_list0,k+jnk) = Tstar(ilagged,:)*dynare_squeeze(aK(jnk-1,:,k+jnk-1));
|
|
end
|
|
end
|
|
end
|
|
aK=aaa;
|
|
ahat=ahat1;
|
|
|
|
% reconstruct P
|
|
if ~isempty(P)
|
|
PP=zeros(M_.endo_nbr,M_.endo_nbr,gend+1);
|
|
PP(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=P;
|
|
if ~options_.heteroskedastic_filter
|
|
DQD=D(~ilagged,:)*Q*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q*transpose(D(~ilagged,:))+D(~ilagged,:)*Q*transpose(C(~ilagged,:)*R);
|
|
DQR=D(~ilagged,:)*Q*transpose(R);
|
|
end
|
|
for k=1:gend+1
|
|
if options_.heteroskedastic_filter
|
|
DQD=D(~ilagged,:)*Q(:,:,k)*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q(:,:,k)*transpose(D(~ilagged,:))+D(~ilagged,:)*Q(:,:,k)*transpose(C(~ilagged,:)*R);
|
|
DQR=D(~ilagged,:)*Q(:,:,k)*transpose(R);
|
|
end
|
|
PP(static_var_list,static_var_list,k)=C(~ilagged,:)*P(:,:,k)*C(~ilagged,:)'+DQD;
|
|
PP(static_var_list,oo_.dr.restrict_var_list,k)=C(~ilagged,:)*P(:,:,k)+DQR;
|
|
PP(oo_.dr.restrict_var_list,static_var_list,k)=transpose(PP(static_var_list,oo_.dr.restrict_var_list,k));
|
|
end
|
|
P=PP;
|
|
clear PP
|
|
end
|
|
|
|
% reconstruct state_uncertainty
|
|
if ~isempty(state_uncertainty)
|
|
mm=size(T,1);
|
|
ss=length(find(static_var_list));
|
|
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr,gend);
|
|
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=state_uncertainty(1:mm,1:mm,:);
|
|
for k=1:gend
|
|
sstate_uncertainty(static_var_list,static_var_list,k)=[C(~ilagged,:) D(~ilagged,:)]*state_uncertainty(:,:,k)*[C(~ilagged,:) D(~ilagged,:)]';
|
|
tmp = [C(~ilagged,:) D(~ilagged,:)]*state_uncertainty(:,:,k);
|
|
sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list,k)=tmp(1:ss,1:mm);
|
|
sstate_uncertainty(oo_.dr.restrict_var_list,static_var_list,k)=transpose(sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list,k));
|
|
end
|
|
state_uncertainty=sstate_uncertainty;
|
|
clear sstate_uncertainty
|
|
end
|
|
|
|
% reconstruct PK
|
|
if ~isempty(PK)
|
|
PP = zeros(options_.nk,M_.endo_nbr,M_.endo_nbr,gend+options_.nk);
|
|
PP(:,oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:) = PK;
|
|
if ~options_.heteroskedastic_filter
|
|
DQD=D(~ilagged,:)*Q*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q*transpose(D(~ilagged,:))+D(~ilagged,:)*Q*transpose(C(~ilagged,:)*R);
|
|
DQR=D(~ilagged,:)*Q*transpose(R);
|
|
for f=1:options_.nk
|
|
for k=1:gend
|
|
PP(f,static_var_list,static_var_list,k+f)=C(~ilagged,:)*squeeze(PK(f,:,:,k+f))*C(~ilagged,:)'+DQD;
|
|
PP(f,static_var_list,oo_.dr.restrict_var_list,k+f)=C(~ilagged,:)*squeeze(PK(f,:,:,k+f))+DQR;
|
|
PP(f,oo_.dr.restrict_var_list,static_var_list,k+f)=transpose(squeeze(PP(f,static_var_list,oo_.dr.restrict_var_list,k+f)));
|
|
end
|
|
end
|
|
end
|
|
PK=PP;
|
|
clear PP
|
|
end
|
|
end
|
|
|
|
bayestopt_.mf = bayestopt_.smoother_var_list(bayestopt_.smoother_mf);
|
|
end
|
|
|
|
function a=set_Kalman_smoother_starting_values(a,M_,oo_,options_)
|
|
% function a=set_Kalman_smoother_starting_values(a,M_,oo_,options_)
|
|
% 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 oo_ [structure] storing the results
|
|
% o options_ [structure] describing the options
|
|
%
|
|
% OUTPUTS
|
|
% o a [double] (p*1) vector of set initial states
|
|
|
|
if isfield(M_,'filter_initial_state') && ~isempty(M_.filter_initial_state)
|
|
state_indices=oo_.dr.order_var(oo_.dr.restrict_columns);
|
|
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(oo_.dr.restrict_columns(ii)) = log(eval(M_.filter_initial_state{state_indices(ii),2})) - log(oo_.dr.ys(state_indices(ii)));
|
|
elseif ~options_.loglinear && ~options_.logged_steady_state
|
|
a(oo_.dr.restrict_columns(ii)) = eval(M_.filter_initial_state{state_indices(ii),2}) - oo_.dr.ys(state_indices(ii));
|
|
else
|
|
error(['The steady state is logged. This should not happen. Please contact the developers'])
|
|
end
|
|
end
|
|
end
|
|
end
|
|
|