v4 added new triangular algorithm for diffuse kalman filter (options_.kalman_algo=4,5)
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1648 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
michel
parent
1a8db86c1b
commit
12436db725
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function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1_Z(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl)
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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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%
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% OUTPUTS
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% alphahat: smoothed state variables
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% etahat: smoothed shocks
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% a: matrix of one step ahead filtered state variables
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% aK: 3D array of k step ahead filtered state variables
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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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%
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% part of DYNARE, copyright Dynare Team (2004-2008)
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% Gnu Public License.
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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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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);
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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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v(:,t)= Y(:,t) - Z*a(:,t);
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F = Z*Pinf(:,:,t)*Z';
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if rcond(F) < crit
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return
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end
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iFinf(:,:,t) = inv(F);
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Kinf(:,:,t) = T*Pinf(:,:,t)*Z'*iFinf(:,:,t);
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a(:,t+1) = T*a(:,t) + Kinf(:,:,t)*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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Linf(:,:,t) = T - Kinf(:,:,t)*Z;
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Fstar(:,:,t) = Z*Pstar(:,:,t)*Z';
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Kstar(:,:,t) = (T*Pstar(:,:,t)*Z'-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*T'-T*Pstar(:,:,t)*Z'*Kinf(:,:,t)'-Kinf(:,:,t)*F*Kstar(:,:,t) + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*T'-T*Pinf(:,:,t)*Z'*Kinf(:,:,t)';
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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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v(:,t) = Y(:,t) - Z*a(:,t);
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P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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F = Z*P(:,:,t)*Z'
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if rcond(F) < crit
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return
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end
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iF(:,:,t) = inv(F);
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K(:,:,t) = T*P(:,:,t)*Z'*iF(:,:,t);
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L(:,:,t) = T-K(:,:,t)*Z;
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a(:,t+1) = T*a(:,t) + K(:,:,t)*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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P(:,:,t+1) = T*P(:,:,t)*transpose(T)-T*P(:,:,t)*Z'*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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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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if t<smpl
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P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
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iF = cat(3,iF(:,:,1:t),repmat(iF_s,[1 1 smpl-t]));
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L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t]));
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K = cat(3,K(:,:,1:t),repmat(T*P_s*Z'*iF_s,[1 1 smpl-t]));
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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) - Z*a(:,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 & t>2
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t = t-1;
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r(:,t-1) = Z'*iF(:,:,t)*v(:,t) + L(:,:,t)'*r(:,t);
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alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t-1);
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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);
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r0(:,d) = r(:,d);
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r1 = zeros(mm,d);
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for t = d:-1:2
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r0(:,t-1) = Linf(:,:,t)'*r0(:,t);
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r1(:,t-1) = Z'*(iFinf(:,:,t)*v(:,t)-Kstar(:,:,t)'*r0(:,t)) + Linf(:,:,t)'*r1(:,t);
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alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t-1) + Pinf(:,:,t)*r1(:,t-1);
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etahat(:,t) = QRt*r0(:,t);
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end
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r0_0 = Linf(:,:,1)'*r0(:,1);
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r1_0 = Z'*(iFinf(:,:,1)*v(:,1)-Kstar(:,:,1)*r0(:,1)) + Linf(:,:,1)'*r1(:,1);
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alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
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etahat(:,1) = QRt*r0(:,1);
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else
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r0 = Z'*iF(:,:,1)*v(:,1) + L(:,:,1)'*r(:,1);
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alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
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etahat(:,1) = QRt*r(:,1);
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end
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@ -0,0 +1,272 @@
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function [alphahat,etahat,a1, aK] = DiffuseKalmanSmoother3_Z(T,Z,R,Q,Pinf1,Pstar1,Y,pp,mm,smpl)
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% function [alphahat,etahat,a1, aK] = DiffuseKalmanSmoother3(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 singular var-cov matrix.
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% Univariate treatment of multivariate time series.
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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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%
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% OUTPUTS
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% alphahat: smoothed state variables
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% etahat: smoothed shocks
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% a1: matrix of one step ahead filtered state variables
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% aK: 3D array of k step ahead filtered state variables
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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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%
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% part of DYNARE, copyright Dynare Team (2004-2008)
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% Gnu Public License.
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% Modified by M. Ratto
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% New output argument aK: 1-step to nk-stpe ahed predictions)
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% New input argument nk: max order of predictions in aK
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% New option options_.diffuse_d where the DKF stops (common with
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% diffuselikelihood3)
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% New icc variable to count number of iterations for Finf steps
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% Pstar % Pinf simmetric
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% New termination of DKF iterations based on options_.diffuse_d
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% Li also stored during DKF iterations !!
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% some bugs corrected in the DKF part of the smoother (Z matrix and
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% alphahat)
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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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a1 = a;
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aK = zeros(nk,mm,smpl+nk);
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if isempty(options_.diffuse_d),
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smpl_diff = 1;
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else
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smpl_diff=rank(Pinf1);
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end
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Fstar = zeros(pp,smpl_diff);
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Finf = zeros(pp,smpl_diff);
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Ki = zeros(mm,pp,smpl);
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Li = zeros(mm,mm,pp,smpl);
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Linf = zeros(mm,mm,pp,smpl_diff);
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L0 = zeros(mm,mm,pp,smpl_diff);
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Kstar = zeros(mm,pp,smpl_diff);
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P = zeros(mm,mm,smpl+1);
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P1 = P;
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Pstar = zeros(spstar(1),spstar(2),smpl_diff+1); Pstar(:,:,1) = Pstar1;
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Pinf = zeros(spinf(1),spinf(2),smpl_diff+1); Pinf(:,:,1) = Pinf1;
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Pstar1 = Pstar;
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Pinf1 = Pinf;
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crit = options_.kalman_tol;
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crit1 = 1.e-6;
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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);
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t = 0;
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icc=0;
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newRank = rank(Pinf(:,:,1),crit1);
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while newRank & t < smpl
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t = t+1;
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a1(:,t) = a(:,t);
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Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
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Pinf(:,:,t)=tril(Pinf(:,:,t))+tril(Pinf(:,:,t),-1)';
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Pstar1(:,:,t) = Pstar(:,:,t);
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Pinf1(:,:,t) = Pinf(:,:,t);
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for i=1:pp
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Zi = Z(i,:);
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v(i,t) = Y(i,t)-Zi*a(:,t);
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Fstar(i,t) = Zi*Pstar(:,:,t)*Zi';
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Finf(i,t) = Zi*Pinf(:,:,t)*Zi';
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Kstar(:,i,t) = Pstar(:,:,t)*Zi;
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if Finf(i,t) > crit & newRank
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icc=icc+1;
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Kinf(:,i,t) = Pinf(:,:,t)*Zi';
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Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
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L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t);
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a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
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Pstar(:,:,t) = Pstar(:,:,t) + ...
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Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
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(Kstar(:,i,t)*Kinf(:,i,t)' +...
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Kinf(:,i,t)*Kstar(:,i,t)')/Finf(i,t);
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Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*Kinf(:,i,t)'/Finf(i,t);
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Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
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Pinf(:,:,t)=tril(Pinf(:,:,t))+tril(Pinf(:,:,t),-1)';
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% new terminiation criteria by M. Ratto
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P0=Pinf(:,:,t);
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if ~isempty(options_.diffuse_d),
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newRank = (icc<options_.diffuse_d);
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if newRank & (any(diag(Z*P0*Z')>crit)==0 & rank(P0,crit1)==0);
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disp('WARNING!! Change in OPTIONS_.DIFFUSE_D in univariate DKF')
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options_.diffuse_d = icc;
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newRank=0;
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end
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else
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newRank = (any(diag(Z*P0*Z')>crit) | rank(P0,crit1));
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if newRank==0,
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options_.diffuse_d = icc;
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end
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end,
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% end new terminiation criteria by M. Ratto
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elseif Fstar(i,t) > crit
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%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
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%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
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%% rank(Pinf)=0. [stéphane,11-03-2004].
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Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
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a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
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Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
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Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
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end
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end
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a(:,t+1) = T*a(:,t);
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for jnk=1:nk,
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aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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end
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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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P0=Pinf(:,:,t+1);
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if newRank,
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newRank = rank(P0,crit1);
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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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Linf = Linf(:,:,:,1:d);
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L0 = L0(:,:,:,1:d);
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Fstar = Fstar(:,1:d);
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Finf = Finf(:,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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Pstar1 = Pstar1(:,:,1:d);
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Pinf1 = Pinf1(:,:,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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a1(:,t) = a(:,t);
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P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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P1(:,:,t) = P(:,:,t);
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for i=1:pp
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Zi = Z(i,:)'
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v(i,t) = Y(i,t) - Zi*a(:,t);
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Fi(i,t) = Zi*P(:,:,t)*Zi';
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Ki(:,i,t) = P(:,:,t)*Zi';
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if Fi(i,t) > crit
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Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
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a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
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P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
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P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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end
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end
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a(:,t+1) = T*a(:,t);
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for jnk=1:nk,
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aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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end
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P(:,:,t+1) = T*P(:,:,t)*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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||||
P_s=tril(P(:,:,t))+tril(P(:,:,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]));
|
||||
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;
|
||||
a1(:,t) = a(:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
a(:,t+1) = T*a(:,t);
|
||||
for jnk=1:nk,
|
||||
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
||||
end
|
||||
end
|
||||
a1(:,t+1) = a(:,t+1);
|
||||
ri=r;
|
||||
t = smpl+1;
|
||||
while t>d+1 & t>2,
|
||||
t = t-1;
|
||||
for i=pp:-1:1
|
||||
if Fi(i,t) > crit
|
||||
ri(:,t) = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri(:,t);
|
||||
end
|
||||
end
|
||||
r(:,t-1) = ri(:,t);
|
||||
alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t-1);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
ri(:,t-1) = T'*ri(:,t);
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d); r0(:,d) = ri(:,d);
|
||||
r1 = zeros(mm,d);
|
||||
for t = d:-1:2
|
||||
for i=pp:-1:1
|
||||
if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination
|
||||
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-1) = r0(:,t);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
r0(:,t-1) = T'*r0(:,t);
|
||||
r1(:,t-1) = T'*r1(:,t);
|
||||
end
|
||||
r0_0 = r0(:,1);
|
||||
r1_0 = r1(:,1);
|
||||
for i=pp:-1:1
|
||||
if Finf(i,1) > crit,
|
||||
r1_0 = Z(i,:)'*v(i,1)/Finf(i,1) + ...
|
||||
L0(:,:,i,1)'*r0_0 + Linf(:,:,i,1)'*r1_0;
|
||||
r0_0 = Linf(:,:,i,1)'*r0_0;
|
||||
elseif Fstar(i,1) > crit, % step needed when Finf=0
|
||||
r0_0=transpose(Z(i,:))/Fstar(i,1)*v(i,1)+Li(:,:,i,1)'*r0_0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a1(:,1) + Pstar1(:,:,1)*r0_0 + Pinf1(:,:,1)*r1_0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
else
|
||||
r0 = ri(:,1);
|
||||
for i=pp:-1:1
|
||||
if Fi(i,1) > crit
|
||||
r0 = Z(i,:)'/Fi(i,1)*v(i,1)+Li(:,:,i,1)'*r0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
|
||||
a=a(:,1:end-1);
|
||||
|
|
@ -1,6 +1,6 @@
|
|||
function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
||||
function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,start)
|
||||
|
||||
% function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
||||
% function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,start)
|
||||
% Computes the diffuse likelihood without measurement error, in the case of a non-singular var-cov matrix
|
||||
%
|
||||
% INPUTS
|
||||
|
|
@ -11,7 +11,6 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
% Pinf: mm*mm diagonal matrix with with q ones and m-q zeros
|
||||
% Pstar: mm*mm variance-covariance matrix with stationary variables
|
||||
% Y: pp*1 vector
|
||||
% trend
|
||||
% start: likelihood evaluation at 'start'
|
||||
%
|
||||
% OUTPUTS
|
||||
|
|
@ -47,7 +46,7 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
reste = 0;
|
||||
while rank(Pinf,crit) & t < smpl
|
||||
t = t+1;
|
||||
v = Y(:,t)-Z*a-trend(:,t);
|
||||
v = Y(:,t)-Z*a;
|
||||
Finf = Z*Pinf*Z';
|
||||
if rcond(Finf) < crit
|
||||
if ~all(abs(Finf(:)) < crit)
|
||||
|
|
@ -68,7 +67,7 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
Kinf = Pinf*Z'*iFinf;
|
||||
Fstar = Z*Pstar*Z';
|
||||
Kstar = (Pstar*Z'-Kinf*Fstar)*iFinf;
|
||||
Pstar = T*(Pstar-Pstar*Z'*Kinf'-Pinf*Z'*Kstar)*T'+QQ;
|
||||
Pstar = T*(Pstar-Pstar*Z'*Kinf'-Pinf*Z'*Kstar')*T'+QQ;
|
||||
Pinf = T*(Pinf-Pinf*Z'*Kinf')*T';
|
||||
a = T*(a+Kinf*v);
|
||||
end
|
||||
|
|
@ -80,7 +79,7 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
F_singular = 1;
|
||||
while notsteady & t < smpl
|
||||
t = t+1;
|
||||
v = Y(:,t)-Z*a-trend(:,t);
|
||||
v = Y(:,t)-Z*a;
|
||||
F = Z*Pstar*Z';
|
||||
oldPstar = Pstar;
|
||||
dF = det(F);
|
||||
|
|
@ -97,7 +96,7 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
lik(t) = log(dF)+v'*iF*v;
|
||||
K = Pstar*Z'*iF;
|
||||
a = T*(a+K*v);
|
||||
Pstar = T*(Pstar-K*Pstar*Z')*T'+QQ;
|
||||
Pstar = T*(Pstar-K*Z*Pstar)*T'+QQ;
|
||||
end
|
||||
notsteady = ~(max(max(abs(Pstar-oldPstar)))<crit);
|
||||
end
|
||||
|
|
@ -108,7 +107,7 @@ function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
|
|||
reste = smpl-t;
|
||||
while t < smpl
|
||||
t = t+1;
|
||||
v = Y(:,t)-Z*a-trend(:,t);
|
||||
v = Y(:,t)-Z*a;
|
||||
a = T*(a+K*v);
|
||||
lik(t) = v*iF*v;
|
||||
end
|
||||
|
|
|
|||
|
|
@ -1,6 +1,6 @@
|
|||
function [LIK, lik] = DiffuseLikelihood3_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)%//Z,T,R,Q,Pinf,Pstar,Y)
|
||||
function [LIK, lik] = DiffuseLikelihood3_Z(T,Z,R,Q,Pinf,Pstar,Y,start)
|
||||
|
||||
% function [LIK, lik] = DiffuseLikelihood3(T,R,Q,Pinf,Pstar,Y,trend,start)
|
||||
% function [LIK, lik] = DiffuseLikelihood3(T,R,Q,Pinf,Pstar,Y,start)
|
||||
% Computes the diffuse likelihood without measurement error, in the case of
|
||||
% a singular var-cov matrix.
|
||||
% Univariate treatment of multivariate time series.
|
||||
|
|
@ -13,7 +13,6 @@ function [LIK, lik] = DiffuseLikelihood3_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)%//Z
|
|||
% Pinf: mm*mm diagonal matrix with with q ones and m-q zeros
|
||||
% Pstar: mm*mm variance-covariance matrix with stationary variables
|
||||
% Y: pp*1 vector
|
||||
% trend
|
||||
% start: likelihood evaluation at 'start'
|
||||
%
|
||||
% OUTPUTS
|
||||
|
|
@ -60,7 +59,7 @@ while newRank & t < smpl
|
|||
t = t+1;
|
||||
for i=1:pp
|
||||
Zi = Z(i,:);
|
||||
v(i) = Y(i,t)-Zi*a-trend(i,t);
|
||||
v(i) = Y(i,t)-Zi*a;
|
||||
Fstar = Zi*Pstar*Zi';
|
||||
Finf = Zi*Pinf*Zi';
|
||||
Kstar = Pstar*Zi';
|
||||
|
|
@ -131,7 +130,7 @@ while notsteady & t < smpl
|
|||
oldP = Pstar;
|
||||
for i=1:pp
|
||||
Zi = Z(i,:);
|
||||
v(i) = Y(i,t) - Zi*a - trend(i,t);
|
||||
v(i) = Y(i,t) - Zi*a;
|
||||
Fi = Zi*Pstar*Zi';
|
||||
if Fi > crit
|
||||
Ki = Pstar*Zi';
|
||||
|
|
@ -151,7 +150,7 @@ while t < smpl
|
|||
Pstar = oldP;
|
||||
for i=1:pp
|
||||
Zi = Z(i,i);
|
||||
v(i) = Y(i,t) - Zi*a - trend(i,t);
|
||||
v(i) = Y(i,t) - Zi*a;
|
||||
Fi = Zi*Pstar*Zi';
|
||||
if Fi > crit
|
||||
Ki = Pstar*Zi';
|
||||
|
|
|
|||
|
|
@ -138,18 +138,71 @@ function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data
|
|||
Pstar = 10*eye(np);
|
||||
Pinf = [];
|
||||
elseif options_.lik_init == 3 % Diffuse Kalman filter
|
||||
Pstar = zeros(np,np);
|
||||
ivs = bayestopt_.restrict_var_list_stationary;
|
||||
R1 = R(ivs,:);
|
||||
Pstar(ivs,ivs) = lyapunov_symm(T(ivs,ivs),R1*Q*R1');
|
||||
% Pinf = bayestopt_.Pinf;
|
||||
% by M. Ratto
|
||||
RR=T(:,bayestopt_.restrict_var_list_nonstationary);
|
||||
i=find(abs(RR)>1.e-10);
|
||||
R0=zeros(size(RR));
|
||||
R0(i)=sign(RR(i));
|
||||
Pinf=R0*R0';
|
||||
% by M. Ratto
|
||||
if options_.kalman_algo < 4
|
||||
Pstar = zeros(np,np);
|
||||
ivs = bayestopt_.restrict_var_list_stationary;
|
||||
R1 = R(ivs,:);
|
||||
Pstar(ivs,ivs) = lyapunov_symm(T(ivs,ivs),R1*Q*R1');
|
||||
% Pinf = bayestopt_.Pinf;
|
||||
% by M. Ratto
|
||||
RR=T(:,bayestopt_.restrict_var_list_nonstationary);
|
||||
i=find(abs(RR)>1.e-10);
|
||||
R0=zeros(size(RR));
|
||||
R0(i)=sign(RR(i));
|
||||
Pinf=R0*R0';
|
||||
% by M. Ratto
|
||||
else
|
||||
[QT,ST] = schur(T);
|
||||
e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
|
||||
[QT,ST] = ordschur(QT,ST,e1);
|
||||
k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
|
||||
nk = length(k);
|
||||
nk1 = nk+1;
|
||||
Pinf = zeros(np,np);
|
||||
Pinf(1:nk,1:nk) = eye(nk);
|
||||
Pstar = zeros(np,np);
|
||||
B = QT'*R*Q*R'*QT;
|
||||
for i=np:-1:nk+2
|
||||
if ST(i,i-1) == 0
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
|
||||
Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
else
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
c1 = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
|
||||
ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
|
||||
c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
|
||||
ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
|
||||
ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
|
||||
-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
|
||||
z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
|
||||
Pstar(nk1:i,i) = z(1:(i-nk));
|
||||
Pstar(nk1:i,i-1) = z(i-nk+1:end);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
|
||||
i = i - 1;
|
||||
end
|
||||
end
|
||||
if i == nk+2
|
||||
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);
|
||||
Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
|
||||
end
|
||||
|
||||
Z = QT(mf,:);
|
||||
R1 = QT'*R;
|
||||
end
|
||||
end
|
||||
%------------------------------------------------------------------------------
|
||||
% 4. Likelihood evaluation
|
||||
|
|
@ -185,6 +238,15 @@ function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data
|
|||
end
|
||||
elseif options_.kalman_algo == 3
|
||||
LIK = DiffuseLikelihood3(T,R,Q,Pinf,Pstar,data,trend,start);
|
||||
elseif options_.kalman_algo == 4
|
||||
data1 = data - trend;
|
||||
LIK = DiffuseLikelihood1_Z(ST,Z,R1,Q,Pinf,Pstar,data1,start);
|
||||
if isinf(LIK)
|
||||
LIK = DiffuseLikelihood3_Z(ST,Z,R1,Q,Pinf,Pstar,data1,start);
|
||||
end
|
||||
elseif options_.kalman_algo == 5
|
||||
data1 = data - trend;
|
||||
LIK = DiffuseLikelihood3_Z(ST,Z,R1,Q,Pinf,Pstar,data1,start);
|
||||
end
|
||||
end
|
||||
if imag(LIK) ~= 0
|
||||
|
|
|
|||
Loading…
Reference in New Issue