diff --git a/matlab/DsgeSmoother.m b/matlab/DsgeSmoother.m
index 09fff8f28917bb1b22e889a257e4d3fa7197c189..1490d848fc810d371f1130b65eab8c333ae26805 100644
--- a/matlab/DsgeSmoother.m
+++ b/matlab/DsgeSmoother.m
@@ -265,7 +265,7 @@ if kalman_algo == 1 || kalman_algo == 3
a_initial = zeros(np,1);
a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
a_initial=T*a_initial; %set state prediction for first Kalman step;
- [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, state_uncertainty0] = missing_DiffuseKalmanSmootherH1_Z(a_initial,ST, ...
+ [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, aalphahat0, state_uncertainty0] = missing_DiffuseKalmanSmootherH1_Z(a_initial,ST, ...
Z,R1,Q,H,Pinf,Pstar, ...
data1,vobs,np,smpl,data_index, ...
options_.nk,kalman_tol,diffuse_kalman_tol,options_.filter_decomposition,options_.smoothed_state_uncertainty,options_.filter_covariance,options_.smoother_redux);
@@ -321,7 +321,7 @@ if kalman_algo == 2 || kalman_algo == 4
a_initial = zeros(np,1);
a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
a_initial=ST*a_initial; %set state prediction for first Kalman step;
- [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, state_uncertainty0, regimes_,TT,RR,CC,TTx,RRx,CCx] = missing_DiffuseKalmanSmootherH3_Z(a_initial,ST, ...
+ [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, aalphahat0, state_uncertainty0, regimes_,TT,RR,CC,TTx,RRx,CCx] = missing_DiffuseKalmanSmootherH3_Z(a_initial,ST, ...
Z,R1,Q,diag(H), ...
Pinf,Pstar,data1,vobs,np,smpl,data_index, ...
options_.nk,kalman_tol,diffuse_kalman_tol, ...
@@ -557,7 +557,9 @@ else
static_var_list(static_var_list) = ~ilagged;
% reconstruct smoothed variables
aaa=zeros(M_.endo_nbr,gend+1);
+ if ~isempty(alphahat0)
aaa(oo_.dr.restrict_var_list,1)=alphahat0;
+ end
aaa(oo_.dr.restrict_var_list,2:end)=alphahat;
for k=1:gend
aaa(static_var_list,k+1) = C(~ilagged,:)*alphahat(:,k)+D(~ilagged,:)*etahat(:,k);
@@ -580,6 +582,9 @@ else
if any(ilagged)
% bbb=zeros(M_.endo_nbr,gend);
% bbb(oo_.dr.restrict_var_list,:)=aahat;
+ if ~isempty(aalphahat0)
+ aaa(static_var_list0,d+1) = Tstar(ilagged,:)*aalphahat0+Rstar(ilagged,:)*eehat(:,d+1);
+ end
for k=d+2:gend
aaa(static_var_list0,k) = Tstar(ilagged,:)*aahat(:,k-1)+Rstar(ilagged,:)*eehat(:,k);
end
diff --git a/matlab/missing_DiffuseKalmanSmootherH1_Z.m b/matlab/missing_DiffuseKalmanSmootherH1_Z.m
index 3cbc664d6f66564f013756073053f9e2cfc79201..cf1430a6abe9bd6cf8f2a9668a4d9e1f917b5cf8 100644
--- a/matlab/missing_DiffuseKalmanSmootherH1_Z.m
+++ b/matlab/missing_DiffuseKalmanSmootherH1_Z.m
@@ -1,4 +1,4 @@
-function [alphahat,epsilonhat,etahat,atilde,P,aK,PK,decomp,V,aalphahat,eetahat,d,alphahat0,V0] = missing_DiffuseKalmanSmootherH1_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag,filter_covariance_flag,smoother_redux)
+function [alphahat,epsilonhat,etahat,atilde,P,aK,PK,decomp,V,aalphahat,eetahat,d,alphahat0,aalphahat0,V0] = missing_DiffuseKalmanSmootherH1_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag,filter_covariance_flag,smoother_redux)
% function [alphahat,epsilonhat,etahat,atilde,P,aK,PK,decomp,V,aalphahat,eetahat,d] = missing_DiffuseKalmanSmootherH1_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag,filter_covariance_flag,smoother_redux)
% Computes the diffuse kalman smoother without measurement error, in the case of a non-singular var-cov matrix.
@@ -141,6 +141,7 @@ else
V=[];
end
alphahat0=[];
+aalphahat0=[];
V0=[];
t = 0;
@@ -276,6 +277,10 @@ while notsteady && t<smpl
eetahat(:,st) = QRt*ri; %DK (2012), eq. 4.63
end
end
+ if t==1
+ ri = T'*ri; %compute r_{t-1}, DK (2012), eq. 4.38 with Z=0
+ aalphahat0 = P(:,:,1)*ri; %DK (2012), eq. 4.35
+ end
end
a(:,t+1) = T*atilde(:,t);
if filter_covariance_flag
diff --git a/matlab/missing_DiffuseKalmanSmootherH3_Z.m b/matlab/missing_DiffuseKalmanSmootherH3_Z.m
index 179b28377da62a00bf890dbda7ecdeafb5964ef0..a5894922aa5815144f5e6bdc7767a99d1611b16b 100644
--- a/matlab/missing_DiffuseKalmanSmootherH3_Z.m
+++ b/matlab/missing_DiffuseKalmanSmootherH3_Z.m
@@ -1,4 +1,4 @@
-function [alphahat,epsilonhat,etahat,a,P1,aK,PK,decomp,V, aalphahat,eetahat,d,alphahat0,V0,varargout] = missing_DiffuseKalmanSmootherH3_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag, filter_covariance_flag, smoother_redux, occbin_)
+function [alphahat,epsilonhat,etahat,a,P1,aK,PK,decomp,V, aalphahat,eetahat,d,alphahat0,aalphahat0,V0,varargout] = missing_DiffuseKalmanSmootherH3_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag, filter_covariance_flag, smoother_redux, occbin_)
% function [alphahat,epsilonhat,etahat,a,P1,aK,PK,decomp,V, aalphahat,eetahat,d] = missing_DiffuseKalmanSmootherH3_Z(a_initial,T,Z,R,Q,H,Pinf1,Pstar1,Y,pp,mm,smpl,data_index,nk,kalman_tol,diffuse_kalman_tol,decomp_flag,state_uncertainty_flag, filter_covariance_flag, smoother_redux, occbin_)
% Computes the diffuse kalman smoother in the case of a singular var-cov matrix.
% Univariate treatment of multivariate time series.
@@ -150,6 +150,7 @@ else
V=[];
end
alphahat0=[];
+aalphahat0=[];
V0=[];
if ~occbin_.status
@@ -389,8 +390,8 @@ while notsteady && t<smpl
if smoother_redux && t>1
aalphahat(:,t-1) = aha(:,1);
- eetahat(:,t) = etaha(:,2);
end
+ eetahat(:,t) = etaha(:,2);
a(:,t) = ax(:,1);
a1(:,t) = a1x(:,2);
a1(:,t+1) = ax(:,2);
@@ -469,6 +470,9 @@ while notsteady && t<smpl
end
ri = T'*ri; % KD (2003), eq. (23), equation for r_{t-1,p_{t-1}}
end
+ if t==1
+ aalphahat0 = P1(:,:,st)*ri;
+ end
end
if isoccbin
if isqvec
diff --git a/tests/kalman_filter_smoother/fs2000_smoother_redux.mod b/tests/kalman_filter_smoother/fs2000_smoother_redux.mod
index 057dd82aeaecbade3b24852f3f0b6683ad0df0c5..ee13d7a2c4401d8edc725c81363fd01c77db13c6 100644
--- a/tests/kalman_filter_smoother/fs2000_smoother_redux.mod
+++ b/tests/kalman_filter_smoother/fs2000_smoother_redux.mod
@@ -115,12 +115,7 @@ if max(merr1)>1.e-12
error('smoother_redux with kalman_algo=1 does not replicate original smoothed static variables!')
end
if max(merr1U)>1.e-12
- for k=1:length(vlist1)
- merr2U(k)=max(abs(oo0.UpdatedVariables.(vlist1{k})(2:end)-oo1.UpdatedVariables.(vlist1{k})(2:end)));
- end
- if max(merr2U)>1.e-12
- error('smoother_redux with kalman_algo=1 does not replicate original updated static variables!')
- end
+ error('smoother_redux with kalman_algo=1 does not replicate original updated static variables!')
end
if max(merr1F)>1.e-12
error('smoother_redux with kalman_algo=1 does not replicate original filtered static variables!')
@@ -177,12 +172,7 @@ if max(merr1)>1.e-12
error('smoother_redux with kalman_algo=2 does not replicate original smoothed static variables!')
end
if max(merr1U)>1.e-12
- for k=1:length(vlist1)
- merr2U(k)=max(abs(oo0.UpdatedVariables.(vlist1{k})(2:end)-oo2.UpdatedVariables.(vlist1{k})(2:end)));
- end
- if max(merr2U)>1.e-12
- error('smoother_redux with kalman_algo=2 does not replicate original updated static variables!')
- end
+ error('smoother_redux with kalman_algo=2 does not replicate original updated static variables!')
end
if max(merr1F)>1.e-12
error('smoother_redux with kalman_algo=2 does not replicate original filtered static variables!')