115 lines
3.7 KiB
Matlab
115 lines
3.7 KiB
Matlab
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 |