302 lines
12 KiB
Matlab
302 lines
12 KiB
Matlab
function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp,trend_addition,state_uncertainty,M_,oo_,options_,bayestopt_] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value,M_,oo_,options_,bayestopt_,estim_params_)
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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] (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 options_ [structure] describing the options
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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 (C) 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 <http://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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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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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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oo_.dr.restrict_var_list = oldoo.restrict_var_list;
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oo_.dr.restrict_columns = oldoo.restrict_columns;
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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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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 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 kalman_algo == 1 || kalman_algo == 3
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty] = 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,options_.smoothed_state_uncertainty);
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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 ~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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Q = blkdiag(Q,H);
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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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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty] = 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,options_.smoothed_state_uncertainty);
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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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