stepan
/
dynare
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
dynare/matlab/missing_DiffuseKalmanSmooth...

283 lines
9.4 KiB
Matlab
Raw Blame History

function [alphahat,epsilonhat,etahat,a,P,aK,PK,decomp] = missing_DiffuseKalmanSmootherH3_Z(T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,decomp_flag)
% function [alphahat,epsilonhat,etahat,a1,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmootherH3_Z(T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,decomp_flag)
% Computes the diffuse kalman smoother without measurement error, in the case of a singular var-cov matrix.
% Univariate treatment of multivariate time series.
%
% INPUTS
% T: mm*mm matrix
% Z: pp*mm matrix
% R: mm*rr matrix
% Q: rr*rr matrix
% H: pp*1 vector of variance of measurement errors
% Pinf1: mm*mm diagonal matrix with with q ones and m-q zeros
% Pstar1: mm*mm variance-covariance matrix with stationary variables
% Y: pp*1 vector
% pp: number of observed variables
% mm: number of state variables
% smpl: sample size
% data_index [cell] 1*smpl cell of column vectors of indices.
% nk number of forecasting periods
% kalman_tol tolerance for zero divider
% decomp_flag if true, compute filter decomposition
%
% OUTPUTS
% alphahat: smoothed state variables (a_{t|T})
% epsilonhat: measurement errors
% etahat: smoothed shocks
% a: matrix of updated variables (a_{t|t})
% aK: 3D array of k step ahead filtered state variables (a_{t+k|t})
% (meaningless for periods 1:d)
% P: 3D array of one-step ahead forecast error variance
% matrices
% PK: 4D array of k-step ahead forecast error variance
% matrices (meaningless for periods 1:d)
% decomp: decomposition of the effect of shocks on filtered values
%
% SPECIAL REQUIREMENTS
% See "Filtering and Smoothing of State Vector for Diffuse State Space
% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
% Analysis, vol. 24(1), pp. 85-98).
% Copyright (C) 2004-2011 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
% Modified by M. Ratto
% New output argument aK: 1-step to nk-stpe ahed predictions)
% New input argument nk: max order of predictions in aK
d = 0;
decomp = [];
spinf = size(Pinf1);
spstar = size(Pstar1);
v = zeros(pp,smpl);
a = zeros(mm,smpl);
a1 = zeros(mm,smpl+1);
aK = zeros(nk,mm,smpl+nk);
Fstar = zeros(pp,smpl);
Finf = zeros(pp,smpl);
Fi = zeros(pp,smpl);
Ki = zeros(mm,pp,smpl);
Kstar = zeros(mm,pp,smpl);
P = zeros(mm,mm,smpl+1);
P1 = P;
PK = zeros(nk,mm,mm,smpl+nk);
Pstar = zeros(spstar(1),spstar(2),smpl); Pstar(:,:,1) = Pstar1;
Pinf = zeros(spinf(1),spinf(2),smpl); Pinf(:,:,1) = Pinf1;
Pstar1 = Pstar;
Pinf1 = Pinf;
crit1 = 1.e-6;
steady = smpl;
rr = size(Q,1); % number of structural shocks
QQ = R*Q*transpose(R);
QRt = Q*transpose(R);
alphahat = zeros(mm,smpl);
etahat = zeros(rr,smpl);
epsilonhat = zeros(rr,smpl);
r = zeros(mm,smpl);
t = 0;
icc=0;
newRank = rank(Pinf(:,:,1),crit1);
while newRank && t < smpl
t = t+1;
a(:,t) = a1(:,t);
Pstar1(:,:,t) = Pstar(:,:,t);
Pinf1(:,:,t) = Pinf(:,:,t);
di = data_index{t}';
for i=di
Zi = Z(i,:);
v(i,t) = Y(i,t)-Zi*a(:,t);
Fstar(i,t) = Zi*Pstar(:,:,t)*Zi' +H(i);
Finf(i,t) = Zi*Pinf(:,:,t)*Zi';
Kstar(:,i,t) = Pstar(:,:,t)*Zi';
if Finf(i,t) > kalman_tol && newRank
icc=icc+1;
Kinf(:,i,t) = Pinf(:,:,t)*Zi';
Kinf_Finf = Kinf(:,i,t)/Finf(i,t);
a(:,t) = a(:,t) + Kinf_Finf*v(i,t);
Pstar(:,:,t) = Pstar(:,:,t) + ...
Kinf(:,i,t)*Kinf_Finf'*(Fstar(i,t)/Finf(i,t)) - ...
Kstar(:,i,t)*Kinf_Finf' - ...
Kinf_Finf*Kstar(:,i,t)';
Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*Kinf(:,i,t)'/Finf(i,t);
elseif Fstar(i,t) > kalman_tol
a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
end
end
if newRank
oldRank = rank(Pinf(:,:,t),crit1);
else
oldRank = 0;
end
a1(:,t+1) = T*a(:,t);
aK(1,:,t+1) = a1(:,t+1);
for jnk=2:nk
aK(jnk,:,t+jnk) = T*dynare_squeeze(aK(jnk-1,:,t+jnk-1));
end
Pstar(:,:,t+1) = T*Pstar(:,:,t)*T'+ QQ;
Pinf(:,:,t+1) = T*Pinf(:,:,t)*T';
P0=Pinf(:,:,t+1);
if newRank,
newRank = rank(Pinf(:,:,t+1),crit1);
end
if oldRank ~= newRank
disp('univariate_diffuse_kalman_filter:: T does influence the rank of Pinf!')
end
end
d = t;
P(:,:,d+1) = Pstar(:,:,d+1);
Fstar = Fstar(:,1:d);
Finf = Finf(:,1:d);
Kstar = Kstar(:,:,1:d);
Pstar = Pstar(:,:,1:d);
Pinf = Pinf(:,:,1:d);
Pstar1 = Pstar1(:,:,1:d);
Pinf1 = Pinf1(:,:,1:d);
notsteady = 1;
while notsteady && t<smpl
t = t+1;
a(:,t) = a1(:,t);
P1(:,:,t) = P(:,:,t);
di = data_index{t}';
for i=di
Zi = Z(i,:);
v(i,t) = Y(i,t) - Zi*a(:,t);
Fi(i,t) = Zi*P(:,:,t)*Zi' + H(i);
Ki(:,i,t) = P(:,:,t)*Zi';
if Fi(i,t) > kalman_tol
a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
end
end
a1(:,t+1) = T*a(:,t);
Pf = P(:,:,t);
aK(1,:,t+1) = a1(:,t+1);
for jnk=1:nk
Pf = T*Pf*T' + QQ;
PK(jnk,:,:,t+jnk) = Pf;
if jnk>1
aK(jnk,:,t+jnk) = T*dynare_squeeze(aK(jnk-1,:,t+jnk-1));
end
end
P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
% notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<kalman_tol);
end
% $$$ P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
% $$$ P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
% $$$ Fi_s = Fi(:,t);
% $$$ Ki_s = Ki(:,:,t);
% $$$ L_s =Li(:,:,:,t);
% $$$ if t<smpl
% $$$ P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
% $$$ P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
% $$$ Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
% $$$ Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
% $$$ Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
% $$$ end
% $$$ while t<smpl
% $$$ t=t+1;
% $$$ a(:,t) = a1(:,t);
% $$$ di = data_index{t}';
% $$$ for i=di
% $$$ Zi = Z(i,:);
% $$$ v(i,t) = Y(i,t) - Zi*a(:,t);
% $$$ if Fi_s(i) > kalman_tol
% $$$ a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
% $$$ end
% $$$ end
% $$$ a1(:,t+1) = T*a(:,t);
% $$$ Pf = P(:,:,t);
% $$$ for jnk=1:nk,
% $$$ Pf = T*Pf*T' + QQ;
% $$$ aK(jnk,:,t+jnk) = T^jnk*a(:,t);
% $$$ PK(jnk,:,:,t+jnk) = Pf;
% $$$ end
% $$$ end
ri=zeros(mm,1);
t = smpl+1;
while t > d+1
t = t-1;
di = flipud(data_index{t})';
for i = di
if Fi(i,t) > kalman_tol
ri = Z(i,:)'/Fi(i,t)*v(i,t)+ri-Ki(:,i,t)'*ri/Fi(i,t)*Z(i,:)';
end
end
r(:,t) = ri;
alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t);
etahat(:,t) = QRt*r(:,t);
ri = T'*ri;
end
if d
r0 = zeros(mm,d);
r0(:,d) = ri;
r1 = zeros(mm,d);
for t = d:-1:1
di = flipud(data_index{t})';
for i = di
if Finf(i,t) > kalman_tol
r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
(Kinf(:,i,t)'*Fstar(i,t)/Finf(i,t)-Kstar(:,i,t)')*r0(:,t)/Finf(i,t)*Z(i,:)' + ...
r1(:,t)-Kinf(:,i,t)'*r1(:,t)/Finf(i,t)*Z(i,:)';
r0(:,t) = r0(:,t)-Kinf(:,i,t)'*r0(:,t)/Finf(i,t)*Z(i,:)';
elseif Fstar(i,t) > kalman_tol % step needed whe Finf == 0
r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+r0(:,t)-(Kstar(:,i,t)'*r0(:,t))/Fstar(i,t)*Z(i,:)';
end
end
alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
r(:,t) = r0(:,t);
etahat(:,t) = QRt*r(:,t);
if t > 1
r0(:,t-1) = T'*r0(:,t);
r1(:,t-1) = T'*r1(:,t);
end
end
end
if decomp_flag
decomp = zeros(nk,mm,rr,smpl+nk);
ZRQinv = inv(Z*QQ*Z');
for t = max(d,1):smpl
ri_d = zeros(mm,1);
di = flipud(data_index{t})';
for i = di
if Fi(i,t) > kalman_tol
ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+ri_d-Ki(:,i,t)'*ri_d/Fi(i,t)*Z(i,:)';
end
end
% calculate eta_tm1t
eta_tm1t = QRt*ri_d;
% calculate decomposition
Ttok = eye(mm,mm);
AAA = P1(:,:,t)*Z'*ZRQinv*Z*R;
for h = 1:nk
BBB = Ttok*AAA;
for j=1:rr
decomp(h,:,j,t+h) = eta_tm1t(j)*BBB(:,j);
end
Ttok = T*Ttok;
end
end
end
epsilonhat = Y - Z*alphahat;
Reference in New Issue View Git Blame Copy Permalink