adding missing data smoother + small corrections
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@2278 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
parent
6a1c5fbd70
commit
706651641f
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@ -264,13 +264,25 @@ function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,d,
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end
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else
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if kalman_algo == 1
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[alphahat,etahat,ahat,aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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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,etahat,ahat,aK] = DiffuseKalmanSmoother1(T,R,Q, ...
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Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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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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[alphahat,etahat,ahat,aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
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if missing_value
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[alphahat,etahat,ahat,aK] = 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,aK] = 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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@ -17,6 +17,6 @@ number_of_observations = length(variable_index);
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if ~missing_observations_counter
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no_more_missing_observations = 0;
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else
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tmp = find(missing_observations_counter>=(gend*nvarobs-number_of_observations))
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tmp = find(missing_observations_counter>=(gend*nvarobs-number_of_observations));
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no_more_missing_observations = tmp(1);
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end
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@ -0,0 +1,207 @@
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function [alphahat,etahat,atilde, aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf,data_index)
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% function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
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% Computes the diffuse kalman smoother without measurement error, in the case of a non-singular var-cov matrix
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%
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% INPUTS
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% T: mm*mm matrix
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% R: mm*rr matrix
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% Q: rr*rr matrix
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% Pinf1: mm*mm diagonal matrix with with q ones and m-q zeros
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% Pstar1: mm*mm variance-covariance matrix with stationary variables
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% Y: pp*1 vector
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% trend
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% pp: number of observed variables
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% mm: number of state variables
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% smpl: sample size
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% mf: observed variables index in the state vector
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% data_index [cell] 1*smpl cell of column vectors of indices.
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%
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% OUTPUTS
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% alphahat: smoothed state variables (a_{t|T})
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% etahat: smoothed shocks
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% atilde: matrix of updated variables (a_{t|t})
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% aK: 3D array of k step ahead filtered state variables (a_{t+k|t})
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% SPECIAL REQUIREMENTS
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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% Copyright (C) 2004-2008 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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% modified by M. Ratto:
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% new output argument aK (1-step to k-step predictions)
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% new options_.nk: the max step ahed prediction in aK (default is 4)
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% new crit1 value for rank of Pinf
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% it is assured that P is symmetric
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global options_
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nk = options_.nk;
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spinf = size(Pinf1);
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spstar = size(Pstar1);
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v = zeros(pp,smpl);
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a = zeros(mm,smpl+1);
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atilde = zeros(mm,smpl);
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aK = zeros(nk,mm,smpl+1);
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iF = zeros(pp,pp,smpl);
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Fstar = zeros(pp,pp,smpl);
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iFinf = zeros(pp,pp,smpl);
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K = zeros(mm,pp,smpl);
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L = zeros(mm,mm,smpl);
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Linf = zeros(mm,mm,smpl);
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Kstar = zeros(mm,pp,smpl);
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P = zeros(mm,mm,smpl+1);
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Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
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Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
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crit = options_.kalman_tol;
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crit1 = 1.e-8;
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steady = smpl;
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rr = size(Q,1);
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QQ = R*Q*transpose(R);
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QRt = Q*transpose(R);
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alphahat = zeros(mm,smpl);
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etahat = zeros(rr,smpl);
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r = zeros(mm,smpl+1);
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Z = zeros(pp,mm);
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for i=1:pp;
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Z(i,mf(i)) = 1;
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end
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t = 0;
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while rank(Pinf(:,:,t+1),crit1) & t<smpl
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t = t+1;
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di = data_index{t};
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if isempty(di)
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atilde(:,t) = a(:,t);
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Linf(:,:,t) = T;
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*T' + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*T';
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else
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mf1 = mf(di);
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v(di,t)= Y(di,t) - a(mf1,t) - trend(di,t);
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if rcond(Pinf(mf1,mf1,t)) < crit
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return
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end
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iFinf(di,di,t) = inv(Pinf(mf1,mf1,t));
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PZI = Pinf(:,mf1,t)*iFinf(di,di,t);
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atilde(:,t) = a(:,t) + PZI*v(di,t);
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Kinf(:,di,t) = T*PZI;
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a(:,t+1) = T*atilde(:,t);
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Linf(:,:,t) = T - Kinf(:,di,t)*Z(di,:);
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Fstar(di,di,t) = Pstar(mf1,mf1,t);
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Kstar(:,di,t) = (T*Pstar(:,mf1,t)-Kinf(:,di,t)*Fstar(di,di,t))*iFinf(di,di,t);
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf1,t)*transpose(Kinf(:,di,t))-Kinf(:,di,t)*Pinf(mf1,mf1,t)*transpose(Kstar(:,di,t)) + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf1,t)* ...
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transpose(Kinf(:,di,t));
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end
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aK(1,:,t+1) = a(:,t+1);
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for jnk=2:nk,
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aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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end
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end
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d = t;
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P(:,:,d+1) = Pstar(:,:,d+1);
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iFinf = iFinf(:,:,1:d);
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Linf = Linf(:,:,1:d);
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Fstar = Fstar(:,:,1:d);
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Kstar = Kstar(:,:,1:d);
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Pstar = Pstar(:,:,1:d);
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Pinf = Pinf(:,:,1:d);
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notsteady = 1;
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while notsteady & t<smpl
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t = t+1;
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P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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di = data_index{t};
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if isempty(di)
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atilde(:,t) = a(:,t);
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L(:,:,t) = T;
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P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
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else
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mf1 = mf(di);
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v(di,t) = Y(di,t) - a(mf1,t) - trend(di,t);
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if rcond(P(mf1,mf1,t)) < crit
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return
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end
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iF(di,di,t) = inv(P(mf1,mf1,t));
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PZI = P(:,mf1,t)*iF(di,di,t);
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atilde(:,t) = a(:,t) + PZI*v(di,t);
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K(:,di,t) = T*PZI;
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L(:,:,t) = T-K(:,di,t)*Z(di,:);
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a(:,t+1) = T*atilde(:,t);
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end
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aK(1,:,t+1) = a(:,t+1);
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for jnk=2:nk,
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aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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end
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P(:,:,t+1) = T*P(:,:,t)*transpose(T)-T*P(:,mf,t)*transpose(K(:,:,t)) + QQ;
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% notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
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end
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% $$$ if t<smpl
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% $$$ PZI_s = PZI;
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% $$$ K_s = K(:,:,t);
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% $$$ iF_s = iF(:,:,t);
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% $$$ P_s = P(:,:,t+1);
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% $$$ t_steady = t+1;
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% $$$ P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
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% $$$ iF = cat(3,iF(:,:,1:t),repmat(inv(P_s(mf,mf)),[1 1 smpl-t_steady+1]));
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% $$$ L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t_steady+1]));
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% $$$ K = cat(3,K(:,:,1:t),repmat(T*P_s(:,mf)*iF_s,[1 1 smpl-t_steady+1]));
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% $$$ end
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% $$$ while t<smpl
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% $$$ t=t+1;
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% $$$ v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
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% $$$ atilde(:,t) = a(:,t) + PZI*v(:,t);
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% $$$ a(:,t+1) = T*a(:,t) + K_s*v(:,t);
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% $$$ aK(1,:,t+1) = a(:,t+1);
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% $$$ for jnk=2:nk,
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% $$$ aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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% $$$ end
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% $$$ end
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t = smpl+1;
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while t>d+1
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t = t-1;
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di = data_index{t};
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if isempty(di)
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r(:,t) = L(:,:,t)'*r(:,t+1);
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else
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r(:,t) = Z(di,:)'*iF(di,di,t)*v(di,t) + L(:,:,t)'*r(:,t+1);
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end
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alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t);
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etahat(:,t) = QRt*r(:,t);
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end
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if d
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r0 = zeros(mm,d+1);
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r0(:,d+1) = r(:,d+1);
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r1 = zeros(mm,d+1);
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for t = d:-1:1
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r0(:,t) = Linf(:,:,t)'*r0(:,t+1);
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di = data_index{t};
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if isempty(di)
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r1(:,t) = Linf(:,:,t)'*r1(:,t+1);
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else
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r1(:,t) = Z(di,:)'*(iFinf(di,di,t)*v(di,t)-Kstar(:,di,t)'*r0(:,t+1)) ...
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+ Linf(:,:,t)'*r1(:,t+1);
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end
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alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t) + Pinf(:,:,t)*r1(:,t);
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etahat(:,t) = QRt*r0(:,t);
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end
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end
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@ -0,0 +1,238 @@
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function [alphahat,etahat,atilde,P,aK,PK,d,decomp] = DiffuseKalmanSmoother1_Z(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl,data_index)
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% function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl)
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% Computes the diffuse kalman smoother without measurement error, in the case of a non-singular var-cov matrix
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%
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% INPUTS
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% T: mm*mm matrix
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% Z: pp*mm matrix
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% R: mm*rr matrix
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% Q: rr*rr matrix
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% Pinf1: mm*mm diagonal matrix with with q ones and m-q zeros
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% Pstar1: mm*mm variance-covariance matrix with stationary variables
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% Y: pp*1 vector
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% pp: number of observed variables
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% mm: number of state variables
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% smpl: sample size
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% data_index [cell] 1*smpl cell of column vectors of indices.
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%
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% OUTPUTS
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% alphahat: smoothed variables (a_{t|T})
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% etahat: smoothed shocks
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% atilde: matrix of updated variables (a_{t|t})
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% aK: 3D array of k step ahead filtered state variables (a_{t+k|t)
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% (meaningless for periods 1:d)
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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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% d: number of periods where filter remains in diffuse part
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% (should be equal to the order of integration of the model)
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% decomp: decomposition of the effect of shocks on filtered values
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%
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% SPECIAL REQUIREMENTS
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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% Copyright (C) 2004-2008 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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% modified by M. Ratto:
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% new output argument aK (1-step to k-step predictions)
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% new options_.nk: the max step ahed prediction in aK (default is 4)
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% new crit1 value for rank of Pinf
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% it is assured that P is symmetric
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global options_
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d = 0;
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decomp = [];
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nk = options_.nk;
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spinf = size(Pinf1);
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spstar = size(Pstar1);
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v = zeros(pp,smpl);
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a = zeros(mm,smpl+1);
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atilde = zeros(mm,smpl);
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aK = zeros(nk,mm,smpl+nk);
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PK = zeros(nk,mm,mm,smpl+nk);
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iF = zeros(pp,pp,smpl);
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Fstar = zeros(pp,pp,smpl);
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iFinf = zeros(pp,pp,smpl);
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K = zeros(mm,pp,smpl);
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L = zeros(mm,mm,smpl);
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Linf = zeros(mm,mm,smpl);
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Kstar = zeros(mm,pp,smpl);
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P = zeros(mm,mm,smpl+1);
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Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
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Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
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crit = options_.kalman_tol;
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crit1 = 1.e-8;
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steady = smpl;
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rr = size(Q,1);
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QQ = R*Q*transpose(R);
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QRt = Q*transpose(R);
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alphahat = zeros(mm,smpl);
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etahat = zeros(rr,smpl);
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r = zeros(mm,smpl+1);
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t = 0;
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while rank(Pinf(:,:,t+1),crit1) & t<smpl
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t = t+1;
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di = data_index{t};
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if isempty(di)
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atilde(:,t) = a(:,t);
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Linf(:,:,t) = T;
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*T' + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*T';
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else
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ZZ = Z(di,:);
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v(di,t)= Y(di,t) - ZZ*a(:,t);
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F = ZZ*Pinf(:,:,t)*ZZ';
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if rcond(F) < crit
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return
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end
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iFinf(di,di,t) = inv(F);
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PZI = Pinf(:,:,t)*ZZ'*iFinf(di,di,t);
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atilde(:,t) = a(:,t) + PZI*v(di,t);
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Kinf(:,di,t) = T*PZI;
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Linf(:,:,t) = T - Kinf(:,di,t)*ZZ;
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Fstar(di,di,t) = ZZ*Pstar(:,:,t)*ZZ';
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Kstar(:,di,t) = (T*Pstar(:,:,t)*ZZ'-Kinf(:,di,t)*Fstar(di,di,t))*iFinf(di,di,t);
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*T'-T*Pstar(:,:,t)*ZZ'*Kinf(:,di,t)'-Kinf(:,di,t)*F*Kstar(:,di,t)' + QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*T'-T*Pinf(:,:,t)*ZZ'*Kinf(:,di,t)';
|
||||
end
|
||||
a(:,t+1) = T*atilde(:,t);
|
||||
aK(1,:,t+1) = a(:,t+1);
|
||||
% isn't a meaningless as long as we are in the diffuse part? MJ
|
||||
for jnk=2:nk,
|
||||
aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
|
||||
end
|
||||
end
|
||||
d = t;
|
||||
P(:,:,d+1) = Pstar(:,:,d+1);
|
||||
iFinf = iFinf(:,:,1:d);
|
||||
Linf = Linf(:,:,1:d);
|
||||
Fstar = Fstar(:,:,1:d);
|
||||
Kstar = Kstar(:,:,1:d);
|
||||
Pstar = Pstar(:,:,1:d);
|
||||
Pinf = Pinf(:,:,1:d);
|
||||
notsteady = 1;
|
||||
while notsteady & t<smpl
|
||||
t = t+1;
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
di = data_index{t};
|
||||
if isempty(di)
|
||||
atilde(:,t) = a(:,t);
|
||||
L(:,:,t) = T;
|
||||
P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
|
||||
else
|
||||
ZZ = Z(di,:);
|
||||
v(di,t) = Y(di,t) - ZZ*a(:,t);
|
||||
F = ZZ*P(:,:,t)*ZZ';
|
||||
if rcond(F) < crit
|
||||
return
|
||||
end
|
||||
iF(di,di,t) = inv(F);
|
||||
PZI = P(:,:,t)*ZZ'*iF(di,di,t);
|
||||
atilde(:,t) = a(:,t) + PZI*v(di,t);
|
||||
K(:,di,t) = T*PZI;
|
||||
L(:,:,t) = T-K(:,di,t)*ZZ;
|
||||
P(:,:,t+1) = T*P(:,:,t)*T'-T*P(:,:,t)*ZZ'*K(:,di,t)' + QQ;
|
||||
end
|
||||
a(:,t+1) = T*atilde(:,t);
|
||||
Pf = P(:,:,t);
|
||||
for jnk=1:nk,
|
||||
Pf = T*Pf*T' + QQ;
|
||||
aK(jnk,:,t+jnk) = T^jnk*atilde(:,t);
|
||||
PK(jnk,:,:,t+jnk) = Pf;
|
||||
end
|
||||
% notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
|
||||
end
|
||||
% $$$ if t<smpl
|
||||
% $$$ PZI_s = PZI;
|
||||
% $$$ K_s = K(:,:,t);
|
||||
% $$$ iF_s = iF(:,:,t);
|
||||
% $$$ P_s = P(:,:,t+1);
|
||||
% $$$ P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
|
||||
% $$$ iF = cat(3,iF(:,:,1:t),repmat(iF_s,[1 1 smpl-t]));
|
||||
% $$$ L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t]));
|
||||
% $$$ K = cat(3,K(:,:,1:t),repmat(T*P_s*Z'*iF_s,[1 1 smpl-t]));
|
||||
% $$$ end
|
||||
% $$$ while t<smpl
|
||||
% $$$ t=t+1;
|
||||
% $$$ v(:,t) = Y(:,t) - Z*a(:,t);
|
||||
% $$$ atilde(:,t) = a(:,t) + PZI*v(:,t);
|
||||
% $$$ a(:,t+1) = T*atilde(:,t);
|
||||
% $$$ Pf = P(:,:,t);
|
||||
% $$$ for jnk=1:nk,
|
||||
% $$$ Pf = T*Pf*T' + QQ;
|
||||
% $$$ aK(jnk,:,t+jnk) = T^jnk*atilde(:,t);
|
||||
% $$$ PK(jnk,:,:,t+jnk) = Pf;
|
||||
% $$$ end
|
||||
% $$$ end
|
||||
t = smpl+1;
|
||||
while t>d+1
|
||||
t = t-1;
|
||||
di = data_index{t};
|
||||
if isempty(di)
|
||||
r(:,t) = L(:,:,t)'*r(:,t+1);
|
||||
else
|
||||
ZZ = Z(di,:);
|
||||
r(:,t) = ZZ'*iF(di,di,t)*v(di,t) + L(:,:,t)'*r(:,t+1);
|
||||
end
|
||||
alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d+1);
|
||||
r0(:,d+1) = r(:,d+1);
|
||||
r1 = zeros(mm,d+1);
|
||||
for t = d:-1:1
|
||||
r0(:,t) = Linf(:,:,t)'*r0(:,t+1);
|
||||
di = data_index{t};
|
||||
if isempty(di)
|
||||
r1(:,t) = Linf(:,:,t)'*r1(:,t+1);
|
||||
else
|
||||
r1(:,t) = Z(di,:)'*(iFinf(di,di,t)*v(di,t)-Kstar(:,di,t)'*r0(:,t+1)) ...
|
||||
+ Linf(:,:,t)'*r1(:,t+1);
|
||||
end
|
||||
alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t) + Pinf(:,:,t)*r1(:,t);
|
||||
etahat(:,t) = QRt*r0(:,t);
|
||||
end
|
||||
end
|
||||
|
||||
if nargout > 7
|
||||
decomp = zeros(nk,mm,rr,smpl+nk);
|
||||
ZRQinv = inv(Z*QQ*Z');
|
||||
for t = max(d,1):smpl
|
||||
ri_d = Z'*iF(:,:,t)*v(:,t);
|
||||
|
||||
% calculate eta_tm1t
|
||||
eta_tm1t = QRt*ri_d;
|
||||
% calculate decomposition
|
||||
Ttok = eye(mm,mm);
|
||||
for h = 1:nk
|
||||
for j=1:rr
|
||||
eta=zeros(rr,1);
|
||||
eta(j) = eta_tm1t(j);
|
||||
decomp(h,:,j,t+h) = T^(h-1)*P(:,:,t)*Z'*ZRQinv*Z*R*eta;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
|
@ -0,0 +1,284 @@
|
|||
function [alphahat,etahat,a, aK] = missing_DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf,data_index)
|
||||
% function [alphahat,etahat,a1, aK] = missing_DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf,data_index)
|
||||
% Computes the diffuse kalman smoother without measurement error, in the case of a singular var-cov matrix.
|
||||
% Univariate treatment of multivariate time series.
|
||||
%
|
||||
% INPUTS
|
||||
% T: mm*mm matrix
|
||||
% R: mm*rr matrix
|
||||
% Q: rr*rr matrix
|
||||
% Pinf1: mm*mm diagonal matrix with with q ones and m-q zeros
|
||||
% Pstar1: mm*mm variance-covariance matrix with stationary variables
|
||||
% Y: pp*1 vector
|
||||
% trend
|
||||
% pp: number of observed variables
|
||||
% mm: number of state variables
|
||||
% smpl: sample size
|
||||
% mf: observed variables index in the state vector
|
||||
% data_index [cell] 1*smpl cell of column vectors of indices.
|
||||
%
|
||||
% OUTPUTS
|
||||
% alphahat: smoothed state variables (a_{t|T})
|
||||
% etahat: smoothed shocks
|
||||
% a: matrix of updated variables (a_{t|t})
|
||||
% aK: 3D array of k step ahead filtered state variables (a_{t+k|t})
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
% See "Filtering and Smoothing of State Vector for Diffuse State Space
|
||||
% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
|
||||
% Analysis, vol. 24(1), pp. 85-98).
|
||||
|
||||
% Copyright (C) 2004-2008 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% Modified by M. Ratto
|
||||
% New output argument aK: 1-step to nk-stpe ahed predictions)
|
||||
% New input argument nk: max order of predictions in aK
|
||||
% New option options_.diffuse_d where the DKF stops (common with
|
||||
% diffuselikelihood3)
|
||||
% New icc variable to count number of iterations for Finf steps
|
||||
% Pstar % Pinf simmetric
|
||||
% New termination of DKF iterations based on options_.diffuse_d
|
||||
% Li also stored during DKF iterations !!
|
||||
% some bugs corrected in the DKF part of the smoother (Z matrix and
|
||||
% alphahat)
|
||||
|
||||
global options_
|
||||
|
||||
nk = options_.nk;
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl);
|
||||
a1 = zeros(mm,smpl+1);
|
||||
aK = zeros(nk,mm,smpl+nk);
|
||||
|
||||
if isempty(options_.diffuse_d),
|
||||
smpl_diff = 1;
|
||||
else
|
||||
smpl_diff=rank(Pinf1);
|
||||
end
|
||||
|
||||
Fstar = zeros(pp,smpl_diff);
|
||||
Finf = zeros(pp,smpl_diff);
|
||||
Ki = zeros(mm,pp,smpl);
|
||||
Li = zeros(mm,mm,pp,smpl);
|
||||
Linf = zeros(mm,mm,pp,smpl_diff);
|
||||
L0 = zeros(mm,mm,pp,smpl_diff);
|
||||
Kstar = zeros(mm,pp,smpl_diff);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
P1 = P;
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl_diff+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl_diff+1); Pinf(:,:,1) = Pinf1;
|
||||
Pstar1 = Pstar;
|
||||
Pinf1 = Pinf;
|
||||
crit = options_.kalman_tol;
|
||||
crit1 = 1.e-6;
|
||||
steady = smpl;
|
||||
rr = size(Q,1);
|
||||
QQ = R*Q*transpose(R);
|
||||
QRt = Q*transpose(R);
|
||||
alphahat = zeros(mm,smpl);
|
||||
etahat = zeros(rr,smpl);
|
||||
r = zeros(mm,smpl+1);
|
||||
|
||||
Z = zeros(pp,mm);
|
||||
for i=1:pp;
|
||||
Z(i,mf(i)) = 1;
|
||||
end
|
||||
|
||||
t = 0;
|
||||
icc=0;
|
||||
newRank = rank(Pinf(:,:,1),crit1);
|
||||
while newRank & t < smpl
|
||||
t = t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
|
||||
Pinf(:,:,t)=tril(Pinf(:,:,t))+transpose(tril(Pinf(:,:,t),-1));
|
||||
Pstar1(:,:,t) = Pstar(:,:,t);
|
||||
Pinf1(:,:,t) = Pinf(:,:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
v(i,t) = Y(i,t)-a(mf(i),t)-trend(i,t);
|
||||
Fstar(i,t) = Pstar(mf(i),mf(i),t);
|
||||
Finf(i,t) = Pinf(mf(i),mf(i),t);
|
||||
Kstar(:,i,t) = Pstar(:,mf(i),t);
|
||||
if Finf(i,t) > crit & newRank, % original MJ: if Finf(i,t) > crit
|
||||
icc=icc+1;
|
||||
Kinf(:,i,t) = Pinf(:,mf(i),t);
|
||||
Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
|
||||
L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Z(i,:)/Finf(i,t);
|
||||
a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
|
||||
Pstar(:,:,t) = Pstar(:,:,t) + ...
|
||||
Kinf(:,i,t)*transpose(Kinf(:,i,t))*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
|
||||
(Kstar(:,i,t)*transpose(Kinf(:,i,t)) +...
|
||||
Kinf(:,i,t)*transpose(Kstar(:,i,t)))/Finf(i,t);
|
||||
Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*transpose(Kinf(:,i,t))/Finf(i,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
|
||||
Pinf(:,:,t)=tril(Pinf(:,:,t))+transpose(tril(Pinf(:,:,t),-1));
|
||||
% new terminiation criteria by M. Ratto
|
||||
P0=Pinf(:,:,t);
|
||||
% newRank = any(diag(P0(mf,mf))>crit);
|
||||
% if newRank==0, id = i; end,
|
||||
if ~isempty(options_.diffuse_d),
|
||||
newRank = (icc<options_.diffuse_d);
|
||||
%if newRank & any(diag(P0(mf,mf))>crit)==0;
|
||||
if newRank & (any(diag(P0(mf,mf))>crit)==0 & rank(P0,crit1)==0);
|
||||
disp('WARNING!! Change in OPTIONS_.DIFFUSE_D in univariate DKF')
|
||||
options_.diffuse_d = icc;
|
||||
newRank=0;
|
||||
end
|
||||
else
|
||||
%newRank = any(diag(P0(mf,mf))>crit);
|
||||
newRank = (any(diag(P0(mf,mf))>crit) | rank(P0,crit1));
|
||||
if newRank==0,
|
||||
options_.diffuse_d = icc;
|
||||
end
|
||||
end,
|
||||
% if newRank==0,
|
||||
% options_.diffuse_d=i; %this is buggy
|
||||
% end
|
||||
% end new terminiation criteria by M. Ratto
|
||||
elseif Fstar(i,t) > crit
|
||||
%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
|
||||
%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
|
||||
%% rank(Pinf)=0. [stéphane,11-03-2004].
|
||||
Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
|
||||
a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
|
||||
Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*transpose(Kstar(:,i,t))/Fstar(i,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
for jnk=1:nk,
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
end
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)+ QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T);
|
||||
P0=Pinf(:,:,t+1);
|
||||
if newRank,
|
||||
%newRank = any(diag(P0(mf,mf))>crit);
|
||||
newRank = rank(P0,crit1);
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
d = t;
|
||||
P(:,:,d+1) = Pstar(:,:,d+1);
|
||||
Linf = Linf(:,:,:,1:d);
|
||||
L0 = L0(:,:,:,1:d);
|
||||
Fstar = Fstar(:,1:d);
|
||||
Finf = Finf(:,1:d);
|
||||
Kstar = Kstar(:,:,1:d);
|
||||
Pstar = Pstar(:,:,1:d);
|
||||
Pinf = Pinf(:,:,1:d);
|
||||
Pstar1 = Pstar1(:,:,1:d);
|
||||
Pinf1 = Pinf1(:,:,1:d);
|
||||
notsteady = 1;
|
||||
while notsteady & t<smpl
|
||||
t = t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
v(i,t) = Y(i,t) - a(mf(i),t) - trend(i,t);
|
||||
Fi(i,t) = P(mf(i),mf(i),t);
|
||||
Ki(:,i,t) = P(:,mf(i),t);
|
||||
if Fi(i,t) > crit
|
||||
Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
|
||||
a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
|
||||
P(:,:,t) = P(:,:,t) - Ki(:,i,t)*transpose(Ki(:,i,t))/Fi(i,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
for jnk=1:nk,
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
end
|
||||
P(:,:,t+1) = T*P(:,:,t)*transpose(T) + QQ;
|
||||
notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
|
||||
end
|
||||
P_s=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
Fi_s = Fi(:,t);
|
||||
Ki_s = Ki(:,:,t);
|
||||
L_s =Li(:,:,:,t);
|
||||
if t<smpl
|
||||
t_steady = t+1;
|
||||
P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
|
||||
Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t_steady+1]));
|
||||
Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t_steady+1]));
|
||||
Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t_steady+1]));
|
||||
end
|
||||
while t<smpl
|
||||
t=t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
v(i,t) = Y(i,t) - a(mf(i),t) - trend(i,t);
|
||||
if Fi_s(i) > crit
|
||||
a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
for jnk=1:nk,
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
end
|
||||
end
|
||||
ri=zeros(mm,1);
|
||||
t = smpl+1;
|
||||
while t>d+1
|
||||
t = t-1;
|
||||
di = flipud(data_index{t})';
|
||||
for i = di
|
||||
if Fi(i,t) > crit
|
||||
ri = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri;
|
||||
end
|
||||
end
|
||||
r(:,t) = ri;
|
||||
alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
ri = T'*ri;
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d);
|
||||
r0(:,d) = ri;
|
||||
r1 = zeros(mm,d);
|
||||
for t = d:-1:1
|
||||
di = flipud(data_index{t})';
|
||||
for i = di
|
||||
if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d),
|
||||
% use of options_.diffuse_d to be sure of DKF termination
|
||||
%r1(:,t) = transpose(Z)*v(:,t)/Finf(i,t) + ... BUG HERE in transpose(Z)
|
||||
r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
|
||||
L0(:,:,i,t)'*r0(:,t) + Linf(:,:,i,t)'*r1(:,t);
|
||||
r0(:,t) = Linf(:,:,i,t)'*r0(:,t);
|
||||
elseif Fstar(i,t) > crit % step needed whe Finf == 0
|
||||
r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t);
|
||||
end
|
||||
end
|
||||
alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
|
||||
r(:,t) = r0(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
if t > 1
|
||||
r0(:,t-1) = T'*r0(:,t);
|
||||
r1(:,t-1) = T'*r1(:,t);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -0,0 +1,316 @@
|
|||
function [alphahat,etahat,a,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3_Z(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl,data_index)
|
||||
% function [alphahat,etahat,a1,P,aK,PK,d,decomp_filt] = missing_DiffuseKalmanSmoother3_Z(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl)
|
||||
% Computes the diffuse kalman smoother without measurement error, in the case of a singular var-cov matrix.
|
||||
% Univariate treatment of multivariate time series.
|
||||
%
|
||||
% INPUTS
|
||||
% T: mm*mm matrix
|
||||
% Z: pp*mm matrix
|
||||
% R: mm*rr matrix
|
||||
% Q: rr*rr matrix
|
||||
% Pinf1: mm*mm diagonal matrix with with q ones and m-q zeros
|
||||
% Pstar1: mm*mm variance-covariance matrix with stationary variables
|
||||
% Y: pp*1 vector
|
||||
% pp: number of observed variables
|
||||
% mm: number of state variables
|
||||
% smpl: sample size
|
||||
% data_index [cell] 1*smpl cell of column vectors of indices.
|
||||
%
|
||||
% OUTPUTS
|
||||
% alphahat: smoothed state variables (a_{t|T})
|
||||
% etahat: smoothed shocks
|
||||
% a: matrix of updated variables (a_{t|t})
|
||||
% aK: 3D array of k step ahead filtered state variables (a_{t+k|t})
|
||||
% (meaningless for periods 1:d)
|
||||
% P: 3D array of one-step ahead forecast error variance
|
||||
% matrices
|
||||
% PK: 4D array of k-step ahead forecast error variance
|
||||
% matrices (meaningless for periods 1:d)
|
||||
% d: number of periods where filter remains in diffuse part
|
||||
% (should be equal to the order of integration of the model)
|
||||
% decomp: decomposition of the effect of shocks on filtered values
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
% See "Filtering and Smoothing of State Vector for Diffuse State Space
|
||||
% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
|
||||
% Analysis, vol. 24(1), pp. 85-98).
|
||||
|
||||
% Copyright (C) 2004-2008 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% Modified by M. Ratto
|
||||
% New output argument aK: 1-step to nk-stpe ahed predictions)
|
||||
% New input argument nk: max order of predictions in aK
|
||||
% New option options_.diffuse_d where the DKF stops (common with
|
||||
% diffuselikelihood3)
|
||||
% New icc variable to count number of iterations for Finf steps
|
||||
% Pstar % Pinf simmetric
|
||||
% New termination of DKF iterations based on options_.diffuse_d
|
||||
% Li also stored during DKF iterations !!
|
||||
% some bugs corrected in the DKF part of the smoother (Z matrix and
|
||||
% alphahat)
|
||||
|
||||
global options_
|
||||
|
||||
d = 0;
|
||||
decomp = [];
|
||||
nk = options_.nk;
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl);
|
||||
a1 = zeros(mm,smpl+1);
|
||||
aK = zeros(nk,mm,smpl+nk);
|
||||
|
||||
if isempty(options_.diffuse_d),
|
||||
smpl_diff = 1;
|
||||
else
|
||||
smpl_diff=rank(Pinf1);
|
||||
end
|
||||
|
||||
Fstar = zeros(pp,smpl_diff);
|
||||
Finf = zeros(pp,smpl_diff);
|
||||
Ki = zeros(mm,pp,smpl);
|
||||
Li = zeros(mm,mm,pp,smpl);
|
||||
Linf = zeros(mm,mm,pp,smpl_diff);
|
||||
L0 = zeros(mm,mm,pp,smpl_diff);
|
||||
Kstar = zeros(mm,pp,smpl_diff);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
P1 = P;
|
||||
aK = zeros(nk,mm,smpl+nk);
|
||||
PK = zeros(nk,mm,mm,smpl+nk);
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl_diff+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl_diff+1); Pinf(:,:,1) = Pinf1;
|
||||
Pstar1 = Pstar;
|
||||
Pinf1 = Pinf;
|
||||
crit = options_.kalman_tol;
|
||||
crit1 = 1.e-6;
|
||||
steady = smpl;
|
||||
rr = size(Q,1); % number of structural shocks
|
||||
QQ = R*Q*transpose(R);
|
||||
QRt = Q*transpose(R);
|
||||
alphahat = zeros(mm,smpl);
|
||||
etahat = zeros(rr,smpl);
|
||||
r = zeros(mm,smpl);
|
||||
|
||||
t = 0;
|
||||
icc=0;
|
||||
newRank = rank(Pinf(:,:,1),crit1);
|
||||
while newRank & t < smpl
|
||||
t = t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
|
||||
Pinf(:,:,t)=tril(Pinf(:,:,t))+tril(Pinf(:,:,t),-1)';
|
||||
Pstar1(:,:,t) = Pstar(:,:,t);
|
||||
Pinf1(:,:,t) = Pinf(:,:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
Zi = Z(i,:);
|
||||
v(i,t) = Y(i,t)-Zi*a(:,t);
|
||||
Fstar(i,t) = Zi*Pstar(:,:,t)*Zi';
|
||||
Finf(i,t) = Zi*Pinf(:,:,t)*Zi';
|
||||
Kstar(:,i,t) = Pstar(:,:,t)*Zi';
|
||||
if Finf(i,t) > crit & newRank
|
||||
icc=icc+1;
|
||||
Kinf(:,i,t) = Pinf(:,:,t)*Zi';
|
||||
Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
|
||||
L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t);
|
||||
a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
|
||||
Pstar(:,:,t) = Pstar(:,:,t) + ...
|
||||
Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
|
||||
(Kstar(:,i,t)*Kinf(:,i,t)' +...
|
||||
Kinf(:,i,t)*Kstar(:,i,t)')/Finf(i,t);
|
||||
Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*Kinf(:,i,t)'/Finf(i,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
|
||||
Pinf(:,:,t)=tril(Pinf(:,:,t))+tril(Pinf(:,:,t),-1)';
|
||||
% new terminiation criteria by M. Ratto
|
||||
P0=Pinf(:,:,t);
|
||||
if ~isempty(options_.diffuse_d),
|
||||
newRank = (icc<options_.diffuse_d);
|
||||
if newRank & (any(diag(Z*P0*Z')>crit)==0 & rank(P0,crit1)==0);
|
||||
disp('WARNING!! Change in OPTIONS_.DIFFUSE_D in univariate DKF')
|
||||
options_.diffuse_d = icc;
|
||||
newRank=0;
|
||||
end
|
||||
else
|
||||
newRank = (any(diag(Z*P0*Z')>crit) | rank(P0,crit1));
|
||||
if newRank==0,
|
||||
options_.diffuse_d = icc;
|
||||
end
|
||||
end,
|
||||
% end new terminiation criteria by M. Ratto
|
||||
elseif Fstar(i,t) > crit
|
||||
%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
|
||||
%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
|
||||
%% rank(Pinf)=0. [stéphane,11-03-2004].
|
||||
Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
|
||||
a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
|
||||
Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
|
||||
Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
for jnk=1:nk,
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
end
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*T'+ QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*T';
|
||||
P0=Pinf(:,:,t+1);
|
||||
if newRank,
|
||||
newRank = rank(P0,crit1);
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
d = t;
|
||||
P(:,:,d+1) = Pstar(:,:,d+1);
|
||||
Linf = Linf(:,:,:,1:d);
|
||||
L0 = L0(:,:,:,1:d);
|
||||
Fstar = Fstar(:,1:d);
|
||||
Finf = Finf(:,1:d);
|
||||
Kstar = Kstar(:,:,1:d);
|
||||
Pstar = Pstar(:,:,1:d);
|
||||
Pinf = Pinf(:,:,1:d);
|
||||
Pstar1 = Pstar1(:,:,1:d);
|
||||
Pinf1 = Pinf1(:,:,1:d);
|
||||
notsteady = 1;
|
||||
while notsteady & t<smpl
|
||||
t = t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
Zi = Z(i,:);
|
||||
v(i,t) = Y(i,t) - Zi*a(:,t);
|
||||
Fi(i,t) = Zi*P(:,:,t)*Zi';
|
||||
Ki(:,i,t) = P(:,:,t)*Zi';
|
||||
if Fi(i,t) > crit
|
||||
Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
|
||||
a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
|
||||
P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
Pf = P(:,:,t);
|
||||
for jnk=1:nk,
|
||||
Pf = T*Pf*T' + QQ;
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
PK(jnk,:,:,t+jnk) = Pf;
|
||||
end
|
||||
P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
|
||||
notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
|
||||
end
|
||||
P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
|
||||
P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
|
||||
Fi_s = Fi(:,t);
|
||||
Ki_s = Ki(:,:,t);
|
||||
L_s =Li(:,:,:,t);
|
||||
if t<smpl
|
||||
P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
|
||||
P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
|
||||
Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
|
||||
Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
|
||||
Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
|
||||
end
|
||||
while t<smpl
|
||||
t=t+1;
|
||||
a(:,t) = a1(:,t);
|
||||
di = data_index{t}';
|
||||
for i=di
|
||||
Zi = Z(i,:);
|
||||
v(i,t) = Y(i,t) - Zi*a(:,t);
|
||||
if Fi_s(i) > crit
|
||||
a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = T*a(:,t);
|
||||
Pf = P(:,:,t);
|
||||
for jnk=1:nk,
|
||||
Pf = T*Pf*T' + QQ;
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
PK(jnk,:,:,t+jnk) = Pf;
|
||||
end
|
||||
end
|
||||
ri=zeros(mm,1);
|
||||
t = smpl+1;
|
||||
while t > d+1
|
||||
t = t-1;
|
||||
di = flipud(data_index{t})';
|
||||
for i = di
|
||||
if Fi(i,t) > crit
|
||||
ri = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri;
|
||||
end
|
||||
end
|
||||
r(:,t) = ri;
|
||||
alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
ri = T'*ri;
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d);
|
||||
r0(:,d) = ri;
|
||||
r1 = zeros(mm,d);
|
||||
for t = d:-1:1
|
||||
di = flipud(data_index{t})';
|
||||
for i = di
|
||||
% if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination
|
||||
if Finf(i,t) > crit
|
||||
r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
|
||||
L0(:,:,i,t)'*r0(:,t) + Linf(:,:,i,t)'*r1(:,t);
|
||||
r0(:,t) = Linf(:,:,i,t)'*r0(:,t);
|
||||
elseif Fstar(i,t) > crit % step needed whe Finf == 0
|
||||
r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t);
|
||||
end
|
||||
end
|
||||
alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
|
||||
r(:,t) = r0(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
if t > 1
|
||||
r0(:,t-1) = T'*r0(:,t);
|
||||
r1(:,t-1) = T'*r1(:,t);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if nargout > 7
|
||||
decomp = zeros(nk,mm,rr,smpl+nk);
|
||||
ZRQinv = inv(Z*QQ*Z');
|
||||
for t = max(d,1):smpl
|
||||
ri_d = zeros(mm,1);
|
||||
di = flipud(data_index{t})';
|
||||
for i = di
|
||||
if Fi(i,t) > crit
|
||||
ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri_d;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate eta_tm1t
|
||||
eta_tm1t = QRt*ri_d;
|
||||
% calculate decomposition
|
||||
Ttok = eye(mm,mm);
|
||||
for h = 1:nk
|
||||
for j=1:rr
|
||||
eta=zeros(rr,1);
|
||||
eta(j) = eta_tm1t(j);
|
||||
decomp(h,:,j,t+h) = Ttok*P1(:,:,t)*Z'*ZRQinv*Z*R*eta;
|
||||
end
|
||||
Ttok = T*Ttok;
|
||||
end
|
||||
end
|
||||
end
|
Loading…
Reference in New Issue