280 lines
10 KiB
Matlab
280 lines
10 KiB
Matlab
function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value)
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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 data [double] (T*n) 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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%
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% OUTPUTS
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% o alphahat [double] (m*T) matrix, smoothed endogenous variables.
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% o etahat [double] (r*T) matrix, smoothed structural shocks (r>n is the umber 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, one step ahead filtered (endogenous) variables.
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% o SteadyState [double] (m*1) vector specifying the steady state level of each endogenous variable.
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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 filtered (endogenous) variables.
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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: 3D array of one-step ahead forecast error variance
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% matrices
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% o PK: 4D array of k-step ahead forecast error variance
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% matrices (meaningless for periods 1:d)
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% o decomp 4D array of shock decomposition of k-step ahead
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% filtered variables
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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 (C) 2006-2014 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 <http://www.gnu.org/licenses/>.
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global bayestopt_ M_ oo_ estim_params_ options_
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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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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_,options_,oo_] = dynare_resolve(M_,options_,oo_);
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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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bayestopt_.mf = bayestopt_.smoother_mf;
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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_coeff = zeros(vobs,1);
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t = options_.trend_coeffs;
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for i=1:length(t)
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if ~isempty(t{i})
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trend_coeff(i) = evalin('base',t{i});
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end
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end
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trend = constant*ones(1,gend)+trend_coeff*(1:gend);
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else
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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_.smoother_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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% C'est ici qu'il faut d<>terminer Pinf et Pstar. Si le mod<6F>le est stationnaire,
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% alors il suffit de poser Pstar comme la solution de l'<27>uation de Lyapounov et
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% Pinf=[].
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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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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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if options_.lyapunov_fp == 1
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Pstar = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, [], options_.debug);
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elseif options_.lyapunov_db == 1
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Pstar = disclyap_fast(T,R*Q*R',options_.lyapunov_doubling_tol);
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elseif options_.lyapunov_srs == 1
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Pstar = lyapunov_symm(T,Q,options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 4, R, options_.debug);
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else
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Pstar = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
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end;
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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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end
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[Z,ST,R1,QT,Pstar,Pinf] = schur_statespace_transformation(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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[err, Pstar] = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(mf,np,vobs)),H);
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mexErrCheck('kalman_steady_state',err);
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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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if options_.lyapunov_fp == 1
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Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, [], options_.debug);
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elseif options_.lyapunov_db == 1
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Pstar_tmp = disclyap_fast(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_doubling_tol);
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elseif options_.lyapunov_srs == 1
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Pstar_tmp = lyapunov_symm(T_tmp,Q,options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 4, R_tmp, options_.debug);
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else
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Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
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end
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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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if kalman_algo == 1 || kalman_algo == 2
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ST = T;
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R1 = R;
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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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end
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if kalman_algo == 1 || kalman_algo == 3
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = missing_DiffuseKalmanSmootherH1_Z(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);
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if isinf(alphahat)
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if kalman_algo == 1
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kalman_algo = 2;
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elseif kalman_algo == 3
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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 estim_params_.ncn
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ST = [ zeros(vobs,vobs) Z; zeros(np,vobs) T];
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ns = size(Q,1);
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R1 = [ eye(vobs) zeros(vobs, ns); zeros(np,vobs) R];
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Q = [H zeros(vobs,ns); zeros(ns,vobs) Q];
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Z = [eye(vobs) zeros(vobs, np)];
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if kalman_algo == 4
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[Z,ST,R1,QT,Pstar,Pinf] = schur_statespace_transformation((1:vobs)',ST,R1,Q,options_.qz_criterium);
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end
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end
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = missing_DiffuseKalmanSmootherH3_Z(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);
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end
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if kalman_algo == 3 || kalman_algo == 4
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alphahat = QT*alphahat;
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ahat = QT*ahat;
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nk = options_.nk;
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for jnk=1:nk
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aK(jnk,:,:) = QT*dynare_squeeze(aK(jnk,:,:));
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for i=1:size(PK,4)
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PK(jnk,:,:,i) = QT*dynare_squeeze(PK(jnk,:,:,i))*QT';
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end
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if options_.filter_decomposition
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for i=1:size(decomp,4)
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decomp(jnk,:,:,i) = QT*dynare_squeeze(decomp(jnk,:,:,i));
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end
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end
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end
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for i=1:size(P,4)
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P(:,:,i) = QT*dynare_squeeze(P(:,:,i))*QT';
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end
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end
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if estim_params_.ncn && (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 = vobs+(1:np);
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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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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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end
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