330 lines
13 KiB
Matlab
330 lines
13 KiB
Matlab
function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,d,decomp] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value)
|
||
% Estimation of the smoothed variables and innovations.
|
||
%
|
||
% INPUTS
|
||
% o xparam1 [double] (p*1) vector of (estimated) parameters.
|
||
% o gend [integer] scalar specifying the number of observations ==> varargin{1}.
|
||
% o data [double] (T*n) matrix of data.
|
||
% o data_index [cell] 1*smpl cell of column vectors of indices.
|
||
% o missing_value 1 if missing values, 0 otherwise
|
||
%
|
||
% OUTPUTS
|
||
% o alphahat [double] (m*T) matrix, smoothed endogenous variables.
|
||
% o etahat [double] (r*T) matrix, smoothed structural shocks (r>n is the umber of shocks).
|
||
% o epsilonhat [double] (n*T) matrix, smoothed measurement errors.
|
||
% o ahat [double] (m*T) matrix, one step ahead filtered (endogenous) variables.
|
||
% o SteadyState [double] (m*1) vector specifying the steady state level of each endogenous variable.
|
||
% o trend_coeff [double] (n*1) vector, parameters specifying the slope of the trend associated to each observed variable.
|
||
% o aK [double] (K,n,T+K) array, k (k=1,...,K) steps ahead filtered (endogenous) variables.
|
||
% o T and R [double] Matrices defining the state equation (T is the (m*m) transition matrix).
|
||
% 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)
|
||
% d: number of periods where filter remains in diffuse part
|
||
% (should be equal to the order of integration of the model)
|
||
%
|
||
% ALGORITHM
|
||
% Diffuse Kalman filter (Durbin and Koopman)
|
||
%
|
||
% SPECIAL REQUIREMENTS
|
||
% None
|
||
|
||
% Copyright (C) 2006-2008 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/>.
|
||
|
||
global bayestopt_ M_ oo_ estim_params_ options_
|
||
|
||
alphahat = [];
|
||
etahat = [];
|
||
epsilonhat = [];
|
||
ahat = [];
|
||
SteadyState = [];
|
||
trend_coeff = [];
|
||
aK = [];
|
||
T = [];
|
||
R = [];
|
||
P = [];
|
||
PK = [];
|
||
d = [];
|
||
decomp = [];
|
||
nobs = size(options_.varobs,1);
|
||
smpl = size(Y,2);
|
||
|
||
set_all_parameters(xparam1);
|
||
|
||
%------------------------------------------------------------------------------
|
||
% 2. call model setup & reduction program
|
||
%------------------------------------------------------------------------------
|
||
[T,R,SteadyState] = dynare_resolve;
|
||
bayestopt_.mf = bayestopt_.mf2;
|
||
if options_.noconstant
|
||
constant = zeros(nobs,1);
|
||
else
|
||
if options_.loglinear == 1
|
||
constant = log(SteadyState(bayestopt_.mfys));
|
||
else
|
||
constant = SteadyState(bayestopt_.mfys);
|
||
end
|
||
end
|
||
trend_coeff = zeros(nobs,1);
|
||
if bayestopt_.with_trend == 1
|
||
trend_coeff = zeros(nobs,1);
|
||
t = options_.trend_coeffs;
|
||
for i=1:length(t)
|
||
if ~isempty(t{i})
|
||
trend_coeff(i) = evalin('base',t{i});
|
||
end
|
||
end
|
||
trend = constant*ones(1,gend)+trend_coeff*(1:gend);
|
||
else
|
||
trend = constant*ones(1,gend);
|
||
end
|
||
start = options_.presample+1;
|
||
np = size(T,1);
|
||
mf = bayestopt_.mf;
|
||
% ------------------------------------------------------------------------------
|
||
% 3. Initial condition of the Kalman filter
|
||
% ------------------------------------------------------------------------------
|
||
%
|
||
% C'est ici qu'il faut d<>terminer Pinf et Pstar. Si le mod<6F>le est stationnaire,
|
||
% alors il suffit de poser Pstar comme la solution de l'<27>uation de Lyapounov et
|
||
% Pinf=[].
|
||
%
|
||
Q = M_.Sigma_e;
|
||
H = M_.H;
|
||
|
||
kalman_algo = options_.kalman_algo;
|
||
if options_.lik_init == 1 % Kalman filter
|
||
if kalman_algo ~= 2
|
||
kalman_algo = 1;
|
||
end
|
||
Pstar = lyapunov_symm(T,R*Q*transpose(R),options_.qz_criterium);
|
||
Pinf = [];
|
||
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
|
||
if kalman_algo ~= 2
|
||
kalman_algo = 1;
|
||
end
|
||
Pstar = 10*eye(np);
|
||
Pinf = [];
|
||
elseif options_.lik_init == 3 % Diffuse Kalman filter
|
||
if kalman_algo ~= 4
|
||
kalman_algo = 3;
|
||
end
|
||
[QT,ST] = schur(T);
|
||
if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
|
||
e1 = abs(my_ordeig(ST)) > 2-options_.qz_criterium;
|
||
else
|
||
e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
|
||
end
|
||
[QT,ST] = ordschur(QT,ST,e1);
|
||
if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
|
||
k = find(abs(my_ordeig(ST)) > 2-options_.qz_criterium);
|
||
else
|
||
k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
|
||
end
|
||
nk = length(k);
|
||
nk1 = nk+1;
|
||
Pinf = zeros(np,np);
|
||
Pinf(1:nk,1:nk) = eye(nk);
|
||
Pstar = zeros(np,np);
|
||
B = QT'*R*Q*R'*QT;
|
||
for i=np:-1:nk+2
|
||
if ST(i,i-1) == 0
|
||
if i == np
|
||
c = zeros(np-nk,1);
|
||
else
|
||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||
end
|
||
q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
|
||
Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
|
||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||
else
|
||
if i == np
|
||
c = zeros(np-nk,1);
|
||
c1 = zeros(np-nk,1);
|
||
else
|
||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
|
||
ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
|
||
c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
|
||
ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
|
||
ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||
end
|
||
q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
|
||
-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
|
||
z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
|
||
Pstar(nk1:i,i) = z(1:(i-nk));
|
||
Pstar(nk1:i,i-1) = z(i-nk+1:end);
|
||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||
Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
|
||
i = i - 1;
|
||
end
|
||
end
|
||
if i == nk+2
|
||
c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
|
||
Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
|
||
end
|
||
|
||
Z = QT(mf,:);
|
||
R1 = QT'*R;
|
||
[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
|
||
k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
|
||
if length(k) > 0
|
||
k1 = EE(:,k);
|
||
dd =ones(nk,1);
|
||
dd(k1) = zeros(length(k1),1);
|
||
Pinf(1:nk,1:nk) = diag(dd);
|
||
end
|
||
end
|
||
% -----------------------------------------------------------------------------
|
||
% 4. Kalman smoother
|
||
% -----------------------------------------------------------------------------
|
||
if any(any(H ~= 0)) % should be replaced by a flag
|
||
if kalman_algo == 1
|
||
[alphahat,epsilonhat,etahat,ahat,aK] = ...
|
||
DiffuseKalmanSmootherH1(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
|
||
if all(alphahat(:)==0)
|
||
kalman_algo = 2;
|
||
if ~estim_params_.ncn
|
||
[alphahat,epsilonhat,etahat,ahat,aK] = ...
|
||
DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
|
||
else
|
||
[alphahat,epsilonhat,etahat,ahat,aK] = ...
|
||
DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
|
||
nobs,np,smpl,mf);
|
||
end
|
||
end
|
||
elseif options_.kalman_algo == 2
|
||
if ~estim_params_.ncn
|
||
[alphahat,epsilonhat,etahat,ahat,aK] = ...
|
||
DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
|
||
else
|
||
[alphahat,epsilonhat,etahat,ahat,aK] = ...
|
||
DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
|
||
nobs,np,smpl,mf);
|
||
end
|
||
elseif kalman_algo == 3 | kalman_algo == 4
|
||
data1 = Y - trend;
|
||
if kalman_algo == 3
|
||
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
|
||
DiffuseKalmanSmootherH1_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
|
||
if all(alphahat(:)==0)
|
||
kalman_algo = 4;
|
||
if ~estim_params_.ncn
|
||
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
|
||
DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
|
||
else
|
||
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
|
||
DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
|
||
nobs,np,smpl);
|
||
end
|
||
end
|
||
else
|
||
if ~estim_params_.ncn
|
||
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
|
||
DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
|
||
nobs,np,smpl);
|
||
else
|
||
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
|
||
DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
|
||
nobs,np,smpl);
|
||
end
|
||
end
|
||
alphahat = QT*alphahat;
|
||
ahat = QT*ahat;
|
||
nk = options_.nk;
|
||
for jnk=1:nk
|
||
aK(jnk,:,:) = QT*squeeze(aK(jnk,:,:));
|
||
for i=1:size(PK,4)
|
||
PK(jnk,:,:,i) = QT*squeeze(PK(jnk,:,:,i))*QT';
|
||
end
|
||
for i=1:size(decomp,4)
|
||
decomp(jnk,:,:,i) = QT*squeeze(decomp(jnk,:,:,i));
|
||
end
|
||
end
|
||
for i=1:size(P,4)
|
||
P(:,:,i) = QT*squeeze(P(:,:,i))*QT';
|
||
end
|
||
end
|
||
else
|
||
if kalman_algo == 1
|
||
if missing_value
|
||
[alphahat,etahat,ahat,aK] = missing_DiffuseKalmanSmoother1(T,R,Q, ...
|
||
Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
|
||
else
|
||
[alphahat,etahat,ahat,aK] = DiffuseKalmanSmoother1(T,R,Q, ...
|
||
Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
|
||
end
|
||
if all(alphahat(:)==0)
|
||
kalman_algo = 2;
|
||
end
|
||
end
|
||
if kalman_algo == 2
|
||
if missing_value
|
||
[alphahat,etahat,ahat,aK] = missing_DiffuseKalmanSmoother3(T,R,Q, ...
|
||
Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
|
||
else
|
||
[alphahat,etahat,ahat,aK] = DiffuseKalmanSmoother3(T,R,Q, ...
|
||
Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
|
||
end
|
||
end
|
||
if kalman_algo == 3
|
||
data1 = Y - trend;
|
||
if missing_value
|
||
[alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother1_Z(ST, ...
|
||
Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
|
||
else
|
||
[alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother1_Z(ST, ...
|
||
Z,R1,Q,Pinf,Pstar, ...
|
||
data1,nobs,np,smpl);
|
||
end
|
||
if all(alphahat(:)==0)
|
||
options_.kalman_algo = 4;
|
||
end
|
||
end
|
||
if kalman_algo == 4
|
||
data1 = Y - trend;
|
||
if missing_value
|
||
[alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3_Z(ST, ...
|
||
Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
|
||
else
|
||
[alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3_Z(ST, ...
|
||
Z,R1,Q,Pinf,Pstar, ...
|
||
data1,nobs,np,smpl);
|
||
end
|
||
end
|
||
if kalman_algo == 3 | kalman_algo == 4
|
||
alphahat = QT*alphahat;
|
||
ahat = QT*ahat;
|
||
nk = options_.nk;
|
||
for jnk=1:nk
|
||
aK(jnk,:,:) = QT*squeeze(aK(jnk,:,:));
|
||
for i=1:size(PK,4)
|
||
PK(jnk,:,:,i) = QT*squeeze(PK(jnk,:,:,i))*QT';
|
||
end
|
||
for i=1:size(decomp,4)
|
||
decomp(jnk,:,:,i) = QT*squeeze(decomp(jnk,:,:,i));
|
||
end
|
||
end
|
||
for i=1:size(P,4)
|
||
P(:,:,i) = QT*squeeze(P(:,:,i))*QT';
|
||
end
|
||
end
|
||
end
|