v4 diffuse smoother: added initialization d=0
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1804 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
michel
parent
f4eda9e12f
commit
e59b3c134f
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@ -46,6 +46,7 @@ function [alphahat,etahat,a,aK,P,PK,d] = DiffuseKalmanSmoother1_Z(T,Z,R,Q,Pinf1,
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global options_
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d = 0;
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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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@ -53,12 +53,14 @@ function [alphahat,etahat,a1,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3_Z(T,Z,R,
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global options_
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d = 0;
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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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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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@ -67,34 +69,34 @@ 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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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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aK = zeros(nk,mm,smpl+nk);
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PK = zeros(nk,mm,mm,smpl+nk);
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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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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); % number of structural shocks
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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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steady = smpl;
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rr = size(Q,1); % number of structural shocks
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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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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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@ -104,21 +106,21 @@ while newRank & t < smpl
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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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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) = 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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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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@ -140,22 +142,22 @@ while newRank & t < smpl
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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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%% 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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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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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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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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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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newRank = rank(P0,crit1);
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end
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end
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@ -244,7 +246,7 @@ while t>d+1 & t>2,
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end
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end
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r(:,t-1) = ri(:,t);
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alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t-1);
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alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t-1);
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etahat(:,t) = QRt*r(:,t);
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ri(:,t-1) = T'*ri(:,t);
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end
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@ -261,9 +263,9 @@ if d
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r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t);
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end
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end
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alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
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r(:,t-1) = r0(:,t);
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etahat(:,t) = QRt*r(:,t);
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alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
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r(:,t-1) = r0(:,t);
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etahat(:,t) = QRt*r(:,t);
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r0(:,t-1) = T'*r0(:,t);
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r1(:,t-1) = T'*r1(:,t);
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end
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@ -278,8 +280,8 @@ if d
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r0_0=Z(i,:)'/Fstar(i,1)*v(i,1)+Li(:,:,i,1)'*r0_0;
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end
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end
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alphahat(:,1) = a1(:,1) + Pstar1(:,:,1)*r0_0 + Pinf1(:,:,1)*r1_0;
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etahat(:,1) = QRt*r(:,1);
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alphahat(:,1) = a1(:,1) + Pstar1(:,:,1)*r0_0 + Pinf1(:,:,1)*r1_0;
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etahat(:,1) = QRt*r(:,1);
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else
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r0 = ri(:,1);
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for i=pp:-1:1
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@ -287,8 +289,8 @@ else
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r0 = Z(i,:)'/Fi(i,1)*v(i,1)+Li(:,:,i,1)'*r0;
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end
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end
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alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
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etahat(:,1) = QRt*r(:,1);
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alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
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etahat(:,1) = QRt*r(:,1);
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end
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a=a(:,1:end-1);
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@ -297,24 +299,24 @@ if nargout > 7
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decomp = zeros(nk,mm,rr,smpl+nk);
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ZRQinv = inv(Z*QQ*Z');
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for t = d:smpl
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ri_d = zeros(mm,1);
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for i=pp:-1:1
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if Fi(i,t) > crit
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ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri_d;
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end
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end
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% calculate eta_tm1t
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eta_tm1t = QRt*ri_d;
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% calculate decomposition
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Ttok = eye(mm,mm);
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for h = 1:nk
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for j=1:rr
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eta=zeros(rr,1);
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eta(j) = eta_tm1t(j);
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decomp(h,:,j,t+h) = Ttok*P1(:,:,t)*Z'*ZRQinv*Z*R*eta;
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end
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Ttok = T*Ttok;
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end
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ri_d = zeros(mm,1);
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for i=pp:-1:1
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if Fi(i,t) > crit
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ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri_d;
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end
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end
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% calculate eta_tm1t
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eta_tm1t = QRt*ri_d;
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% calculate decomposition
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Ttok = eye(mm,mm);
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for h = 1:nk
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for j=1:rr
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eta=zeros(rr,1);
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eta(j) = eta_tm1t(j);
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decomp(h,:,j,t+h) = Ttok*P1(:,:,t)*Z'*ZRQinv*Z*R*eta;
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end
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Ttok = T*Ttok;
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end
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end
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end
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