330 lines
13 KiB
Matlab
330 lines
13 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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% P: 3D array of one-step ahead forecast error variance
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% matrices
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% PK: 4D array of k-step ahead forecast error variance
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% matrices (meaningless for periods 1:d)
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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) 2006-2010 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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nobs = size(options_.varobs,1);
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smpl = size(Y,2);
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set_all_parameters(xparam1);
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%------------------------------------------------------------------------------
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% 2. call model setup & reduction program
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%------------------------------------------------------------------------------
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[T,R,SteadyState] = dynare_resolve(bayestopt_.smoother_var_list,...
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bayestopt_.smoother_restrict_columns,[]);
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bayestopt_.mf = bayestopt_.smoother_mf;
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if options_.noconstant
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constant = zeros(nobs,1);
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else
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if options_.loglinear == 1
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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(nobs,1);
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if bayestopt_.with_trend == 1
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trend_coeff = zeros(nobs,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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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_symm(T,R*Q*transpose(R),options_.qz_criterium,options_.lyapunov_complex_threshold);
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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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[QT,ST] = schur(T);
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e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
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[QT,ST] = ordschur(QT,ST,e1);
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k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
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nk = length(k);
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nk1 = nk+1;
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Pinf = zeros(np,np);
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Pinf(1:nk,1:nk) = eye(nk);
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Pstar = zeros(np,np);
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B = QT'*R*Q*R'*QT;
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for i=np:-1:nk+2
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if ST(i,i-1) == 0
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if i == np
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c = zeros(np-nk,1);
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else
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c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
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ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
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end
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q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
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Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
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Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
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else
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if i == np
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c = zeros(np-nk,1);
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c1 = zeros(np-nk,1);
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else
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c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
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ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
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ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
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c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
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ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
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ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
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end
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q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
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-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
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z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
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Pstar(nk1:i,i) = z(1:(i-nk));
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Pstar(nk1:i,i-1) = z(i-nk+1:end);
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Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
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Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
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i = i - 1;
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end
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end
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if i == nk+2
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c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
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Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
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end
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Z = QT(mf,:);
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R1 = QT'*R;
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[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
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k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
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if length(k) > 0
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k1 = EE(:,k);
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dd =ones(nk,1);
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dd(k1) = zeros(length(k1),1);
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Pinf(1:nk,1:nk) = diag(dd);
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end
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end
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kalman_tol = options_.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 any(any(H ~= 0)) % should be replaced by a flag
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if kalman_algo == 1
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = ...
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kalman_smoother(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
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if all(alphahat(:)==0)
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kalman_algo = 2;
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if ~estim_params_.ncn
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[alphahat,epsilonhat,etahat,ahat,aK] = ...
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DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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else
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[alphahat,epsilonhat,etahat,ahat,aK] = ...
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DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
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nobs,np,smpl,mf);
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end
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end
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elseif options_.kalman_algo == 2
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if ~estim_params_.ncn
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[alphahat,epsilonhat,etahat,ahat,aK] = ...
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DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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else
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[alphahat,epsilonhat,etahat,ahat,aK] = ...
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DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
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nobs,np,smpl,mf);
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end
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elseif kalman_algo == 3 | kalman_algo == 4
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data1 = Y - trend;
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if kalman_algo == 3
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
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DiffuseKalmanSmootherH1_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
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if all(alphahat(:)==0)
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kalman_algo = 4;
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if ~estim_params_.ncn
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
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DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
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else
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
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DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
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nobs,np,smpl);
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end
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end
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else
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if ~estim_params_.ncn
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
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DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
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nobs,np,smpl);
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else
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
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DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
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nobs,np,smpl);
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end
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end
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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*squeeze(aK(jnk,:,:));
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for i=1:size(PK,4)
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PK(jnk,:,:,i) = QT*squeeze(PK(jnk,:,:,i))*QT';
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end
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for i=1:size(decomp,4)
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decomp(jnk,:,:,i) = QT*squeeze(decomp(jnk,:,:,i));
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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*squeeze(P(:,:,i))*QT';
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end
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end
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else
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H = 0;
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if kalman_algo == 1
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if missing_value
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[alphahat,etahat,ahat,aK] = missing_DiffuseKalmanSmoother1(T,R,Q, ...
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Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
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else
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[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = ...
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kalman_smoother(T,R,Q,H,Pstar,data1,start,mf,kalman_tol,riccati_tol);
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end
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if all(alphahat(:)==0)
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kalman_algo = 2;
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end
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end
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if kalman_algo == 2
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if missing_value
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3(T,R,Q, ...
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Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
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else
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3(T,R,Q, ...
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Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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end
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end
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if kalman_algo == 3
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data1 = Y - trend;
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if missing_value
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother1_Z(ST, ...
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Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
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else
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother1_Z(ST, ...
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Z,R1,Q,Pinf,Pstar, ...
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data1,nobs,np,smpl);
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end
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if all(alphahat(:)==0)
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options_.kalman_algo = 4;
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end
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end
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if kalman_algo == 4
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data1 = Y - trend;
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if missing_value
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3_Z(ST, ...
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Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
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else
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[alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3_Z(ST, ...
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Z,R1,Q,Pinf,Pstar, ...
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data1,nobs,np,smpl);
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end
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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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% $$$ if M_.exo_nbr<2 % Fix the crash of Dynare when the estimated model has only one structural shock (problem with
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% $$$ % the squeeze function, that does not affect 2D arrays).
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% $$$ size_decomp = 0;
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% $$$ else
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% $$$ size_decomp = size(decomp,4);
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% $$$ end
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for jnk=1:nk
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aK(jnk,:,:) = QT*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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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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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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end
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