v4 DiffuseKalmanSmoother*.m: merged with version 3 to add k-period ahead forecast
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@645 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
michel
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f090d02f9b
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1c14cd2685
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@ -1,115 +1,137 @@
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function [alphahat,etahat,a] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
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% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
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%
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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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global options_
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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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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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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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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),crit) & 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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if rcond(Pinf(mf,mf,t)) < crit
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return
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end
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iFinf(:,:,t) = inv(Pinf(mf,mf,t));
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Kinf(:,:,t) = T*Pinf(:,mf,t)*iFinf(:,:,t);
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a(:,t+1) = T*a(:,t) + Kinf(:,:,t)*v(:,t);
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Linf(:,:,t) = T - Kinf(:,:,t)*Z;
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Fstar(:,:,t) = Pstar(mf,mf,t);
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Kstar(:,:,t) = (T*Pstar(:,mf,t)-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf,t)*transpose(Kinf(:,:,t))-Kinf(:,:,t)*Pinf(mf,mf,t)*transpose(Kstar(:,:,t)) + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf,t)*transpose(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) - a(mf,t) - trend(:,t);
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if rcond(P(mf,mf,t)) < crit
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return
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end
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iF(:,:,t) = inv(P(mf,mf,t));
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K(:,:,t) = T*P(:,mf,t)*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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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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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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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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a(:,t+1) = T*a(:,t) + K_s*v(:,t);
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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) = transpose(Z)*iF(:,:,t)*v(:,t) + transpose(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); 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) = transpose(Linf(:,:,t))*r0(:,t);
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r1(:,t-1) = transpose(Z)*(iFinf(:,:,t)*v(:,t)-transpose(Kstar(:,:,t))*r0(:,t)) + transpose(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 = transpose(Linf(:,:,1))*r0(:,1);
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r1_0 = transpose(Z)*(iFinf(:,:,1)*v(:,1)-transpose(Kstar(:,:,1))*r0(:,1)) + transpose(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 = transpose(Z)*iF(:,:,1)*v(:,1) + transpose(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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function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
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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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%
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% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
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%
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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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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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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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v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
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if rcond(Pinf(mf,mf,t)) < crit
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return
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end
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iFinf(:,:,t) = inv(Pinf(mf,mf,t));
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Kinf(:,:,t) = T*Pinf(:,mf,t)*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) = Pstar(mf,mf,t);
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Kstar(:,:,t) = (T*Pstar(:,mf,t)-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
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Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf,t)*transpose(Kinf(:,:,t))-Kinf(:,:,t)*Pinf(mf,mf,t)*transpose(Kstar(:,:,t)) + QQ;
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Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf,t)*transpose(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) - a(mf,t) - trend(:,t);
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P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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if rcond(P(mf,mf,t)) < crit
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return
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end
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iF(:,:,t) = inv(P(mf,mf,t));
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K(:,:,t) = T*P(:,mf,t)*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(:,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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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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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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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) = transpose(Z)*iF(:,:,t)*v(:,t) + transpose(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); 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) = transpose(Linf(:,:,t))*r0(:,t);
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r1(:,t-1) = transpose(Z)*(iFinf(:,:,t)*v(:,t)-transpose(Kstar(:,:,t))*r0(:,t)) + transpose(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 = transpose(Linf(:,:,1))*r0(:,1);
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r1_0 = transpose(Z)*(iFinf(:,:,1)*v(:,1)-transpose(Kstar(:,:,1))*r0(:,1)) + transpose(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 = transpose(Z)*iF(:,:,1)*v(:,1) + transpose(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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@ -1,185 +1,253 @@
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function [alphahat,etahat,a1] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
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% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
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%
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% See "Fast Filtering and Smoothing for Multivariate State Space
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% Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series
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% Analysis, vol. 21(3), pp. 281-296).
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global options_;
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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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Fstar = zeros(pp,smpl);
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Finf = zeros(pp,smpl);
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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);
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L0 = zeros(mm,mm,pp,smpl);
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Kstar = zeros(mm,pp,smpl);
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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+1); Pstar(:,:,1) = Pstar1;
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Pinf = zeros(spinf(1),spinf(2),smpl+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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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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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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newRank = rank(Pinf(:,:,1),crit);
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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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Pstar1(:,:,t) = Pstar(:,:,t);
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Pinf1(:,:,t) = Pinf(:,:,t);
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for i=1:pp
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v(i,t) = Y(i,t)-a(mf(i),t)-trend(i,t);
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Fstar(i,t) = Pstar(mf(i),mf(i),t);
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Finf(i,t) = Pinf(mf(i),mf(i),t);
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Kstar(:,i,t) = Pstar(:,mf(i),t);
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if Finf(i,t) > crit
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Kinf(:,i,t) = Pinf(:,mf(i),t);
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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))*Z(i,:)/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)*transpose(Kinf(:,i,t))*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
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(Kstar(:,i,t)*transpose(Kinf(:,i,t)) +...
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Kinf(:,i,t)*transpose(Kstar(:,i,t)))/Finf(i,t);
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Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*transpose(Kinf(:,i,t))/Finf(i,t);
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else %% 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].
|
||||
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);
|
||||
end
|
||||
end
|
||||
a(:,t+1) = T*a(:,t);
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)+ QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T);
|
||||
P0=Pinf(:,:,t+1);
|
||||
newRank = ~all(abs(P0(:))<crit);
|
||||
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;
|
||||
a1(:,t) = a(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
a(:,t+1) = T*a(:,t);
|
||||
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;
|
||||
a1(:,t) = a(:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
a(:,t+1) = T*a(:,t);
|
||||
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)=transpose(Z(i,:))/Fi(i,t)*v(i,t)+transpose(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) = transpose(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,
|
||||
r1(:,t) = transpose(Z)*v(:,t)/Finf(i,t) + ...
|
||||
transpose(L0(:,:,i,t))*r0(:,t) + transpose(Linf(:,:,i,t))*r1(:,t);
|
||||
r0(:,t) = transpose(Linf(:,:,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) = transpose(T)*r0(:,t);
|
||||
r1(:,t-1) = transpose(T)*r1(:,t);
|
||||
end
|
||||
r0_0 = r0(:,1);
|
||||
r1_0 = r1(:,1);
|
||||
for i=pp:-1:1
|
||||
if Finf(i,1) > crit,
|
||||
r1_0 = transpose(Z)*v(:,1)/Finf(i,1) + ...
|
||||
transpose(L0(:,:,i,1))*r0_0 + transpose(Linf(:,:,i,1))*r1_0;
|
||||
r0_0 = transpose(Linf(:,:,i,1))*r0_0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
else
|
||||
r0 = ri(:,1);
|
||||
for i=pp:-1:1
|
||||
if Fi(i,1) > crit
|
||||
r0=transpose(Z(i,:))/Fi(i,1)*v(i,1)+transpose(Li(:,:,i,1))*r0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
function [alphahat,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
|
||||
% 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 global variable id_ 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 id_
|
||||
% Li also stored during DKF iterations !!
|
||||
% some bugs corrected in the DKF part of the smoother (Z matrix and
|
||||
% alphahat)
|
||||
%
|
||||
% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
|
||||
%
|
||||
% See "Fast Filtering and Smoothing for Multivariate State Space
|
||||
% Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series
|
||||
% Analysis, vol. 21(3), pp. 281-296).
|
||||
|
||||
global options_
|
||||
|
||||
nk = options_.nk;
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl+1);
|
||||
a1 = a;
|
||||
aK = zeros(nk,mm,smpl+nk);
|
||||
Fstar = zeros(pp,smpl);
|
||||
Finf = zeros(pp,smpl);
|
||||
Ki = zeros(mm,pp,smpl);
|
||||
Li = zeros(mm,mm,pp,smpl);
|
||||
Linf = zeros(mm,mm,pp,smpl);
|
||||
L0 = zeros(mm,mm,pp,smpl);
|
||||
Kstar = zeros(mm,pp,smpl);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
P1 = P;
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl+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);
|
||||
|
||||
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;
|
||||
a1(:,t) = a(:,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);
|
||||
for i=1:pp
|
||||
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;
|
||||
end
|
||||
% end new terminiation criteria by M. Ratto
|
||||
else
|
||||
%% 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
|
||||
a(:,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;
|
||||
a1(:,t) = a(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
a(:,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;
|
||||
a1(:,t) = a(:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
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)=transpose(Z(i,:))/Fi(i,t)*v(i,t)+transpose(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) = transpose(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) = transpose(Z)*v(:,t)/Finf(i,t) + ... BUG HERE in transpose(Z)
|
||||
r1(:,t) = transpose(Z(i,:))*v(i,t)/Finf(i,t) + ...
|
||||
transpose(L0(:,:,i,t))*r0(:,t) + transpose(Linf(:,:,i,t))*r1(:,t);
|
||||
r0(:,t) = transpose(Linf(:,:,i,t))*r0(:,t);
|
||||
elseif Fstar(i,t) > crit % step needed whe Finf == 0
|
||||
r0(:,t)=transpose(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) = transpose(T)*r0(:,t);
|
||||
r1(:,t-1) = transpose(T)*r1(:,t);
|
||||
end
|
||||
r0_0 = r0(:,1);
|
||||
r1_0 = r1(:,1);
|
||||
for i=pp:-1:1
|
||||
if Finf(i,1) > crit,
|
||||
%r1_0 = transpose(Z)*v(:,1)/Finf(i,1) + ... %bug with Z here
|
||||
r1_0 = transpose(Z(i,:))*v(i,1)/Finf(i,1) + ...
|
||||
transpose(L0(:,:,i,1))*r0_0 + transpose(Linf(:,:,i,1))*r1_0;
|
||||
r0_0 = transpose(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) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0; %this line is buggy
|
||||
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=transpose(Z(i,:))/Fi(i,1)*v(i,1)+transpose(Li(:,:,i,1))*r0;
|
||||
end
|
||||
end
|
||||
%alphahat(:,1) = a(:,1) + P(:,:,1)*r0; % this line is buggy
|
||||
alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,117 +1,138 @@
|
|||
function [alphahat,epsilonhat,etahat,a] = DiffuseKalmanSmootherH1(T,R,Q,H,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
|
||||
% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
|
||||
%
|
||||
% 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).
|
||||
|
||||
global options_;
|
||||
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl+1);
|
||||
iF = zeros(pp,pp,smpl);
|
||||
Fstar = zeros(pp,pp,smpl);
|
||||
iFinf = zeros(pp,pp,smpl);
|
||||
K = zeros(mm,pp,smpl);
|
||||
L = zeros(mm,mm,smpl);
|
||||
Linf = zeros(mm,mm,smpl);
|
||||
Kstar = zeros(mm,pp,smpl);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
|
||||
crit = options_.kalman_tol;
|
||||
steady = smpl;
|
||||
rr = size(Q,1);
|
||||
QQ = R*Q*transpose(R);
|
||||
QRt = Q*transpose(R);
|
||||
alphahat = zeros(mm,smpl);
|
||||
etahat = zeros(rr,smpl);
|
||||
epsilonhat = zeros(size(Y));
|
||||
r = zeros(mm,smpl);
|
||||
|
||||
Z = zeros(pp,mm);
|
||||
for i=1:pp;
|
||||
Z(i,mf(i)) = 1;
|
||||
end
|
||||
|
||||
t = 0;
|
||||
while rank(Pinf(:,:,t+1),crit) & t<smpl
|
||||
t = t+1;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
if rcond(Pinf(mf,mf,t)) < crit
|
||||
return
|
||||
end
|
||||
iFinf(:,:,t) = inv(Pinf(mf,mf,t));
|
||||
Kinf(:,:,t) = T*Pinf(:,mf,t)*iFinf(:,:,t);
|
||||
a(:,t+1) = T*a(:,t) + Kinf(:,:,t)*v(:,t);
|
||||
Linf(:,:,t) = T - Kinf(:,:,t)*Z;
|
||||
Fstar(:,:,t) = Pstar(mf,mf,t) + H;
|
||||
Kstar(:,:,t) = (T*Pstar(:,mf,t)-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf,t)*transpose(Kinf(:,:,t))-Kinf(:,:,t)*Pinf(mf,mf,t)*transpose(Kstar(:,:,t)) + QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf,t)*transpose(Kinf(:,:,t));
|
||||
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;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
if rcond(P(mf,mf,t)+H) < crit
|
||||
return
|
||||
end
|
||||
iF(:,:,t) = inv(P(mf,mf,t)+H);
|
||||
K(:,:,t) = T*P(:,mf,t)*iF(:,:,t);
|
||||
L(:,:,t) = T-K(:,:,t)*Z;
|
||||
a(:,t+1) = T*a(:,t) + K(:,:,t)*v(:,t);
|
||||
P(:,:,t+1) = T*P(:,:,t)*transpose(T)-T*P(:,mf,t)*transpose(K(:,:,t)) + QQ;
|
||||
notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
|
||||
end
|
||||
K_s = K(:,:,t);
|
||||
iF_s = iF(:,:,t);
|
||||
P_s = P(:,:,t+1);
|
||||
if t<smpl
|
||||
t_steady = t+1;
|
||||
P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
|
||||
iF = cat(3,iF(:,:,1:t),repmat(inv(P_s(mf,mf) + H),[1 1 smpl-t_steady+1]));
|
||||
L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t_steady+1]));
|
||||
K = cat(3,K(:,:,1:t),repmat(T*P_s(:,mf)*iF_s,[1 1 smpl-t_steady+1]));
|
||||
end
|
||||
while t<smpl
|
||||
t=t+1;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
a(:,t+1) = T*a(:,t) + K_s*v(:,t);
|
||||
end
|
||||
t = smpl+1;
|
||||
while t>d+1 & t>2
|
||||
t = t-1;
|
||||
r(:,t-1) = transpose(Z)*iF(:,:,t)*v(:,t) + transpose(L(:,:,t))*r(:,t);
|
||||
alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t-1);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d); r0(:,d) = r(:,d);
|
||||
r1 = zeros(mm,d);
|
||||
for t = d:-1:2
|
||||
r0(:,t-1) = transpose(Linf(:,:,t))*r0(:,t);
|
||||
r1(:,t-1) = transpose(Z)*(iFinf(:,:,t)*v(:,t)-transpose(Kstar(:,:,t))*r0(:,t)) + transpose(Linf(:,:,t))*r1(:,t);
|
||||
alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t-1) + Pinf(:,:,t)*r1(:,t-1);
|
||||
etahat(:,t) = QRt*r0(:,t);
|
||||
end
|
||||
r0_0 = transpose(Linf(:,:,1))*r0(:,1);
|
||||
r1_0 = transpose(Z)*(iFinf(:,:,1)*v(:,1)-transpose(Kstar(:,:,1))*r0(:,1)) + transpose(Linf(:,:,1))*r1(:,1);
|
||||
alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
|
||||
etahat(:,1) = QRt*r0(:,1);
|
||||
else
|
||||
r0 = transpose(Z)*iF(:,:,1)*v(:,1) + transpose(L(:,:,1))*r(:,1);
|
||||
alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
epsilonhat = Y-alphahat(mf,:)-trend;
|
||||
function [alphahat,epsilonhat,etahat,a, aK] = DiffuseKalmanSmootherH1(T,R,Q,H,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
|
||||
% modified by M. Ratto:
|
||||
% new output argument aK (1-step to k-step predictions)
|
||||
% new options_.nk: the max step ahed prediction in aK (default is 4)
|
||||
% new crit1 value for rank of Pinf
|
||||
% it is assured that P is symmetric
|
||||
%
|
||||
% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
|
||||
%
|
||||
% 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).
|
||||
|
||||
global options_
|
||||
|
||||
nk = options_.nk;
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl+1);
|
||||
iF = zeros(pp,pp,smpl);
|
||||
Fstar = zeros(pp,pp,smpl);
|
||||
iFinf = zeros(pp,pp,smpl);
|
||||
K = zeros(mm,pp,smpl);
|
||||
L = zeros(mm,mm,smpl);
|
||||
Linf = zeros(mm,mm,smpl);
|
||||
Kstar = zeros(mm,pp,smpl);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
|
||||
crit = options_.kalman_tol;
|
||||
crit1 = 1.e-8;
|
||||
steady = smpl;
|
||||
rr = size(Q,1);
|
||||
QQ = R*Q*transpose(R);
|
||||
QRt = Q*transpose(R);
|
||||
alphahat = zeros(mm,smpl);
|
||||
etahat = zeros(rr,smpl);
|
||||
epsilonhat = zeros(size(Y));
|
||||
r = zeros(mm,smpl);
|
||||
|
||||
Z = zeros(pp,mm);
|
||||
for i=1:pp;
|
||||
Z(i,mf(i)) = 1;
|
||||
end
|
||||
|
||||
t = 0;
|
||||
while rank(Pinf(:,:,t+1),crit1) & t<smpl
|
||||
t = t+1;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
if rcond(Pinf(mf,mf,t)) < crit
|
||||
return
|
||||
end
|
||||
iFinf(:,:,t) = inv(Pinf(mf,mf,t));
|
||||
Kinf(:,:,t) = T*Pinf(:,mf,t)*iFinf(:,:,t);
|
||||
a(:,t+1) = T*a(:,t) + Kinf(:,:,t)*v(:,t);
|
||||
aK(1,:,t+1) = a(:,t+1);
|
||||
for jnk=2:nk,
|
||||
aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
|
||||
end
|
||||
Linf(:,:,t) = T - Kinf(:,:,t)*Z;
|
||||
Fstar(:,:,t) = Pstar(mf,mf,t) + H;
|
||||
Kstar(:,:,t) = (T*Pstar(:,mf,t)-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf,t)*transpose(Kinf(:,:,t))-Kinf(:,:,t)*Pinf(mf,mf,t)*transpose(Kstar(:,:,t)) + QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf,t)*transpose(Kinf(:,:,t));
|
||||
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;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
if rcond(P(mf,mf,t) + H) < crit
|
||||
return
|
||||
end
|
||||
iF(:,:,t) = inv(P(mf,mf,t) + H);
|
||||
K(:,:,t) = T*P(:,mf,t)*iF(:,:,t);
|
||||
L(:,:,t) = T-K(:,:,t)*Z;
|
||||
a(:,t+1) = T*a(:,t) + K(:,:,t)*v(:,t);
|
||||
aK(1,:,t+1) = a(:,t+1);
|
||||
for jnk=2:nk,
|
||||
aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
|
||||
end
|
||||
P(:,:,t+1) = T*P(:,:,t)*transpose(T)-T*P(:,mf,t)*transpose(K(:,:,t)) + QQ;
|
||||
notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
|
||||
end
|
||||
K_s = K(:,:,t);
|
||||
iF_s = iF(:,:,t);
|
||||
P_s = P(:,:,t+1);
|
||||
if t<smpl
|
||||
t_steady = t+1;
|
||||
P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
|
||||
iF = cat(3,iF(:,:,1:t),repmat(inv(P_s(mf,mf)+H),[1 1 smpl-t_steady+1]));
|
||||
L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t_steady+1]));
|
||||
K = cat(3,K(:,:,1:t),repmat(T*P_s(:,mf)*iF_s,[1 1 smpl-t_steady+1]));
|
||||
end
|
||||
while t<smpl
|
||||
t=t+1;
|
||||
v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
|
||||
a(:,t+1) = T*a(:,t) + K_s*v(:,t);
|
||||
aK(1,:,t+1) = a(:,t+1);
|
||||
for jnk=2:nk,
|
||||
aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
|
||||
end
|
||||
end
|
||||
t = smpl+1;
|
||||
while t>d+1 & t>2
|
||||
t = t-1;
|
||||
r(:,t-1) = transpose(Z)*iF(:,:,t)*v(:,t) + transpose(L(:,:,t))*r(:,t);
|
||||
alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t-1);
|
||||
etahat(:,t) = QRt*r(:,t);
|
||||
end
|
||||
if d
|
||||
r0 = zeros(mm,d); r0(:,d) = r(:,d);
|
||||
r1 = zeros(mm,d);
|
||||
for t = d:-1:2
|
||||
r0(:,t-1) = transpose(Linf(:,:,t))*r0(:,t);
|
||||
r1(:,t-1) = transpose(Z)*(iFinf(:,:,t)*v(:,t)-transpose(Kstar(:,:,t))*r0(:,t)) + transpose(Linf(:,:,t))*r1(:,t);
|
||||
alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t-1) + Pinf(:,:,t)*r1(:,t-1);
|
||||
etahat(:,t) = QRt*r0(:,t);
|
||||
end
|
||||
r0_0 = transpose(Linf(:,:,1))*r0(:,1);
|
||||
r1_0 = transpose(Z)*(iFinf(:,:,1)*v(:,1)-transpose(Kstar(:,:,1))*r0(:,1)) + transpose(Linf(:,:,1))*r1(:,1);
|
||||
alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
|
||||
etahat(:,1) = QRt*r0(:,1);
|
||||
else
|
||||
r0 = transpose(Z)*iF(:,:,1)*v(:,1) + transpose(L(:,:,1))*r(:,1);
|
||||
alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
epsilonhat = Y-alphahat(mf,:)-trend;
|
||||
|
|
|
|||
|
|
@ -1,186 +1,255 @@
|
|||
function [alphahat,epsilonhat,etahat,a1] = DiffuseKalmanSmootherH3(T,R,Q,H,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
|
||||
% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
|
||||
%
|
||||
% See "Fast Filtering and Smoothing for Multivariate State Space
|
||||
% Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series
|
||||
% Analysis, vol. 21(3), pp. 281-296).
|
||||
global options_
|
||||
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl+1);
|
||||
a1 = a;
|
||||
Fstar = zeros(pp,smpl);
|
||||
Finf = zeros(pp,smpl);
|
||||
Ki = zeros(mm,pp,smpl);
|
||||
Li = zeros(mm,mm,pp,smpl);
|
||||
Linf = zeros(mm,mm,pp,smpl);
|
||||
L0 = zeros(mm,mm,pp,smpl);
|
||||
Kstar = zeros(mm,pp,smpl);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
P1 = P;
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
|
||||
Pstar1 = Pstar;
|
||||
Pinf1 = Pinf;
|
||||
crit = options_.kalman_tol;
|
||||
steady = smpl;
|
||||
rr = size(Q,1);
|
||||
QQ = R*Q*transpose(R);
|
||||
QRt = Q*transpose(R);
|
||||
alphahat = zeros(mm,smpl);
|
||||
etahat = zeros(rr,smpl);
|
||||
epsilonhat = zeros(size(Y));
|
||||
r = zeros(mm,smpl);
|
||||
|
||||
Z = zeros(pp,mm);
|
||||
for i=1:pp;
|
||||
Z(i,mf(i)) = 1;
|
||||
end
|
||||
|
||||
t = 0;
|
||||
newRank = rank(Pinf(:,:,1),crit);
|
||||
while newRank & t < smpl
|
||||
t = t+1;
|
||||
a1(:,t) = a(:,t);
|
||||
Pstar1(:,:,t) = Pstar(:,:,t);
|
||||
Pinf1(:,:,t) = Pinf(:,:,t);
|
||||
for i=1:pp
|
||||
v(i,t) = Y(i,t)-a(mf(i),t)-trend(i,t);
|
||||
Fstar(i,t) = Pstar(mf(i),mf(i),t)+H(i,i);
|
||||
Finf(i,t) = Pinf(mf(i),mf(i),t);
|
||||
Kstar(:,i,t) = Pstar(:,mf(i),t);
|
||||
if Finf(i,t) > crit
|
||||
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);
|
||||
else %% 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].
|
||||
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);
|
||||
end
|
||||
end
|
||||
a(:,t+1) = T*a(:,t);
|
||||
Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)+ QQ;
|
||||
Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T);
|
||||
P0=Pinf(:,:,t+1);
|
||||
newRank = ~all(abs(P0(:))<crit);
|
||||
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;
|
||||
a1(:,t) = a(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
for i=1:pp
|
||||
v(i,t) = Y(i,t) - a(mf(i),t) - trend(i,t);
|
||||
Fi(i,t) = P(mf(i),mf(i),t)+H(i,i);
|
||||
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
|
||||
a(:,t+1) = T*a(:,t);
|
||||
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;
|
||||
a1(:,t) = a(:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
a(:,t+1) = T*a(:,t);
|
||||
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)=transpose(Z(i,:))/Fi(i,t)*v(i,t)+transpose(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) = transpose(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,
|
||||
r1(:,t) = transpose(Z)*v(:,t)/Finf(i,t) + ...
|
||||
transpose(L0(:,:,i,t))*r0(:,t) + transpose(Linf(:,:,i,t))*r1(:,t);
|
||||
r0(:,t) = transpose(Linf(:,:,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) = transpose(T)*r0(:,t);
|
||||
r1(:,t-1) = transpose(T)*r1(:,t);
|
||||
end
|
||||
r0_0 = r0(:,1);
|
||||
r1_0 = r1(:,1);
|
||||
for i=pp:-1:1
|
||||
if Finf(i,1) > crit,
|
||||
r1_0 = transpose(Z)*v(:,1)/Finf(i,1) + ...
|
||||
transpose(L0(:,:,i,1))*r0_0 + transpose(Linf(:,:,i,1))*r1_0;
|
||||
r0_0 = transpose(Linf(:,:,i,1))*r0_0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
else
|
||||
r0 = ri(:,1);
|
||||
for i=pp:-1:1
|
||||
if Fi(i,1) > crit
|
||||
r0=transpose(Z(i,:))/Fi(i,1)*v(i,1)+transpose(Li(:,:,i,1))*r0;
|
||||
end
|
||||
end
|
||||
alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
epsilonhat = Y-alphahat(mf,:)-trend;
|
||||
function [alphahat,epsilonhat,etahat,a1, aK] = DiffuseKalmanSmootherH3(T,R,Q,H,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
|
||||
% 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 global variable id_ 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 id_
|
||||
% Li also stored during DKF iterations !!
|
||||
% some bugs corrected in the DKF part of the smoother (Z matrix and
|
||||
% alphahat)
|
||||
%
|
||||
% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
|
||||
%
|
||||
% See "Fast Filtering and Smoothing for Multivariate State Space
|
||||
% Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series
|
||||
% Analysis, vol. 21(3), pp. 281-296).
|
||||
|
||||
global options_
|
||||
|
||||
nk = options_.nk;
|
||||
spinf = size(Pinf1);
|
||||
spstar = size(Pstar1);
|
||||
v = zeros(pp,smpl);
|
||||
a = zeros(mm,smpl+1);
|
||||
a1 = a;
|
||||
aK = zeros(nk,mm,smpl+nk);
|
||||
Fstar = zeros(pp,smpl);
|
||||
Finf = zeros(pp,smpl);
|
||||
Ki = zeros(mm,pp,smpl);
|
||||
Li = zeros(mm,mm,pp,smpl);
|
||||
Linf = zeros(mm,mm,pp,smpl);
|
||||
L0 = zeros(mm,mm,pp,smpl);
|
||||
Kstar = zeros(mm,pp,smpl);
|
||||
P = zeros(mm,mm,smpl+1);
|
||||
P1 = P;
|
||||
Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
|
||||
Pinf = zeros(spinf(1),spinf(2),smpl+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);
|
||||
epsilonhat = zeros(size(Y));
|
||||
r = zeros(mm,smpl);
|
||||
|
||||
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;
|
||||
a1(:,t) = a(:,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);
|
||||
for i=1:pp
|
||||
v(i,t) = Y(i,t)-a(mf(i),t)-trend(i,t);
|
||||
Fstar(i,t) = Pstar(mf(i),mf(i),t) + H(i,i);
|
||||
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, options_.diffuse_d = 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;
|
||||
end
|
||||
% end new terminiation criteria by M. Ratto
|
||||
else
|
||||
%% 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
|
||||
a(:,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;
|
||||
a1(:,t) = a(:,t);
|
||||
P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
|
||||
P1(:,:,t) = P(:,:,t);
|
||||
for i=1:pp
|
||||
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) + H(i,i);
|
||||
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
|
||||
a(:,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;
|
||||
a1(:,t) = a(:,t);
|
||||
for i=1:pp
|
||||
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
|
||||
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)=transpose(Z(i,:))/Fi(i,t)*v(i,t)+transpose(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) = transpose(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) = transpose(Z)*v(:,t)/Finf(i,t) + ... BUG HERE in transpose(Z)
|
||||
r1(:,t) = transpose(Z(i,:))*v(i,t)/Finf(i,t) + ...
|
||||
transpose(L0(:,:,i,t))*r0(:,t) + transpose(Linf(:,:,i,t))*r1(:,t);
|
||||
r0(:,t) = transpose(Linf(:,:,i,t))*r0(:,t);
|
||||
elseif Fstar(i,t) > crit % step needed whe Finf == 0
|
||||
r0(:,t)=transpose(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) = transpose(T)*r0(:,t);
|
||||
r1(:,t-1) = transpose(T)*r1(:,t);
|
||||
end
|
||||
r0_0 = r0(:,1);
|
||||
r1_0 = r1(:,1);
|
||||
for i=pp:-1:1
|
||||
if Finf(i,1) > crit,
|
||||
%r1_0 = transpose(Z)*v(:,1)/Finf(i,1) + ... %bug with Z here
|
||||
r1_0 = transpose(Z(i,:))*v(i,1)/Finf(i,1) + ...
|
||||
transpose(L0(:,:,i,1))*r0_0 + transpose(Linf(:,:,i,1))*r1_0;
|
||||
r0_0 = transpose(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) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0; %this line is buggy
|
||||
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=transpose(Z(i,:))/Fi(i,1)*v(i,1)+transpose(Li(:,:,i,1))*r0;
|
||||
end
|
||||
end
|
||||
%alphahat(:,1) = a(:,1) + P(:,:,1)*r0; % this line is buggy
|
||||
alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
|
||||
etahat(:,1) = QRt*r(:,1);
|
||||
end
|
||||
epsilonhat = Y-alphahat(mf,:)-trend;
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue