322 lines
13 KiB
Matlab
322 lines
13 KiB
Matlab
function [LIK, lik, a, P] = missing_observations_kalman_filter(data_index,number_of_observations,no_more_missing_observations,Y,start,last,a,P,kalman_tol,riccati_tol,rescale_prediction_error_covariance,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods,occbin_)
|
|
% [LIK, lik, a, P] = missing_observations_kalman_filter(data_index,number_of_observations,no_more_missing_observations,Y,start,last,a,P,kalman_tol,riccati_tol,rescale_prediction_error_covariance,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods,occbin_)
|
|
% Computes the likelihood of a state space model in the case with missing observations.
|
|
%
|
|
% INPUTS
|
|
% data_index [cell] 1*smpl cell of column vectors of indices.
|
|
% number_of_observations [integer] scalar.
|
|
% no_more_missing_observations [integer] scalar.
|
|
% Y [double] pp*smpl matrix of data.
|
|
% start [integer] scalar, index of the first observation.
|
|
% last [integer] scalar, index of the last observation.
|
|
% a [double] pp*1 vector, levels of the predicted initial state variables (E_{0}(alpha_1)).
|
|
% P [double] pp*pp matrix, covariance matrix of the initial state vector.
|
|
% kalman_tol [double] scalar, tolerance parameter (rcond).
|
|
% riccati_tol [double] scalar, tolerance parameter (riccati iteration).
|
|
% presample [integer] scalar, presampling if strictly positive.
|
|
% T [double] mm*mm transition matrix of the state equation.
|
|
% Q [double] rr*rr covariance matrix of the structural innovations.
|
|
% R [double] mm*rr matrix, mapping structural innovations to state variables.
|
|
% H [double] pp*pp (or 1*1 =0 if no measurement error) covariance matrix of the measurement errors.
|
|
% Z [integer] pp*1 vector of indices for the observed variables.
|
|
% mm [integer] scalar, dimension of the state vector.
|
|
% pp [integer] scalar, number of observed variables.
|
|
% rr [integer] scalar, number of structural innovations.
|
|
%
|
|
% OUTPUTS
|
|
% LIK [double] scalar, MINUS loglikelihood
|
|
% lik [double] vector, density of observations in each period.
|
|
% a [double] mm*1 vector, current estimate of the state vector tomorrow (E_{T}(alpha_{T+1})).
|
|
% P [double] mm*mm matrix, covariance matrix of the states.
|
|
%
|
|
%
|
|
% NOTES
|
|
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
|
|
|
% Copyright © 2004-2023 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 <https://www.gnu.org/licenses/>.
|
|
|
|
% Set defaults
|
|
if nargin<20
|
|
Zflag = 0;
|
|
diffuse_periods = 0;
|
|
end
|
|
|
|
if nargin<21
|
|
diffuse_periods = 0;
|
|
end
|
|
|
|
if isempty(Zflag)
|
|
Zflag = 0;
|
|
end
|
|
|
|
if isempty(diffuse_periods)
|
|
diffuse_periods = 0;
|
|
end
|
|
|
|
if isequal(H,0)
|
|
H = zeros(pp,pp);
|
|
end
|
|
|
|
% Get sample size.
|
|
smpl = last-start+1;
|
|
|
|
% Initialize some variables.
|
|
dF = 1;
|
|
isqvec = false;
|
|
if ndim(Q)>2
|
|
Qvec = Q;
|
|
Q=Q(:,:,1);
|
|
isqvec = true;
|
|
end
|
|
QQ = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
|
|
t = start; % Initialization of the time index.
|
|
lik = zeros(smpl,1); % Initialization of the vector gathering the densities.
|
|
LIK = Inf; % Default value of the log likelihood.
|
|
oldK = Inf;
|
|
notsteady = 1;
|
|
F_singular = true;
|
|
s = 0;
|
|
rescale_prediction_error_covariance0=rescale_prediction_error_covariance;
|
|
if occbin_.status
|
|
base_regime = struct();
|
|
Qt = repmat(Q,[1 1 3]);
|
|
a0 = zeros(mm,last);
|
|
a1 = zeros(mm,last);
|
|
P0 = zeros(mm,mm,last);
|
|
P1 = zeros(mm,mm,last);
|
|
vv = zeros(pp,last);
|
|
|
|
options_=occbin_.info{1};
|
|
dr=occbin_.info{2};
|
|
endo_steady_state=occbin_.info{3};
|
|
exo_steady_state=occbin_.info{4};
|
|
exo_det_steady_state=occbin_.info{5};
|
|
M_=occbin_.info{6};
|
|
occbin_options=occbin_.info{7};
|
|
occbin_options.opts_simul.SHOCKS = [];
|
|
opts_regime.regime_history = occbin_options.opts_regime.init_regime_history;
|
|
opts_regime.binding_indicator = occbin_options.opts_regime.init_binding_indicator;
|
|
if t>1
|
|
first_period_occbin_update = max(t+1,options_.occbin.likelihood.first_period_occbin_update);
|
|
else
|
|
first_period_occbin_update = options_.occbin.likelihood.first_period_occbin_update;
|
|
end
|
|
if isempty(opts_regime.binding_indicator) && isempty(opts_regime.regime_history)
|
|
opts_regime.binding_indicator=zeros(last+2,M_.occbin.constraint_nbr);
|
|
end
|
|
[~, ~, ~, regimes_] = occbin.check_regimes([], [], [], opts_regime, M_, options_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
|
|
if length(occbin_.info)>7
|
|
TT=occbin_.info{8};
|
|
RR=occbin_.info{9};
|
|
CC=occbin_.info{10};
|
|
T0=occbin_.info{11};
|
|
R0=occbin_.info{12};
|
|
TT = cat(3,TT,T);
|
|
RR = cat(3,RR,R);
|
|
CC = cat(2,CC,zeros(mm,1));
|
|
if size(TT,3)<(last+1)
|
|
TT=repmat(T,1,1,last+1);
|
|
RR=repmat(R,1,1,last+1);
|
|
CC=repmat(zeros(mm,1),1,last+1);
|
|
end
|
|
|
|
end
|
|
if M_.occbin.constraint_nbr==1
|
|
base_regime.regime = 0;
|
|
base_regime.regimestart = 1;
|
|
else
|
|
base_regime.regime1 = 0;
|
|
base_regime.regimestart1 = 1;
|
|
base_regime.regime2 = 0;
|
|
base_regime.regimestart2 = 1;
|
|
end
|
|
else
|
|
first_period_occbin_update = inf;
|
|
C=0;
|
|
end
|
|
|
|
while notsteady && t<=last
|
|
if occbin_.status
|
|
a1(:,t) = a;
|
|
P1(:,:,t) = P;
|
|
C = CC(:,t+1);
|
|
R = RR(:,:,t+1);
|
|
T = TT(:,:,t+1);
|
|
if ~(isqvec)
|
|
QQ = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
|
|
end
|
|
if t==1
|
|
Pinit = P1(:,:,1);
|
|
ainit = a1(:,1);
|
|
end
|
|
end
|
|
s = t-start+1;
|
|
d_index = data_index{t};
|
|
if isqvec
|
|
QQ = R*Qvec(:,:,t+1)*transpose(R);
|
|
end
|
|
if isempty(d_index)
|
|
a = T*a;
|
|
P = T*P*transpose(T)+QQ;
|
|
else
|
|
% Compute the prediction error and its variance
|
|
if Zflag
|
|
z = Z(d_index,:);
|
|
v = Y(d_index,t)-z*a;
|
|
F = z*P*z' + H(d_index,d_index);
|
|
else
|
|
z = Z(d_index);
|
|
v = Y(d_index,t) - a(z);
|
|
F = P(z,z) + H(d_index,d_index);
|
|
end
|
|
badly_conditioned_F = false;
|
|
if rescale_prediction_error_covariance
|
|
sig=sqrt(diag(F));
|
|
if any(diag(F)<kalman_tol) || rcond(F./(sig*sig'))<kalman_tol
|
|
badly_conditioned_F = true;
|
|
end
|
|
else
|
|
if rcond(F)<kalman_tol
|
|
sig=sqrt(diag(F));
|
|
if any(diag(F)<kalman_tol) || rcond(F./(sig*sig'))<kalman_tol
|
|
badly_conditioned_F = true;
|
|
else
|
|
rescale_prediction_error_covariance=1;
|
|
end
|
|
% badly_conditioned_F = true;
|
|
end
|
|
end
|
|
if badly_conditioned_F && (~occbin_.status || (occbin_.status && t<first_period_occbin_update))
|
|
% if ~all(abs(F(:))<kalman_tol), then use univariate filter, otherwise this is a
|
|
% pathological case and the draw is discarded
|
|
return
|
|
else
|
|
F_singular = false;
|
|
end
|
|
if ~occbin_.status || (occbin_.status && (options_.occbin.likelihood.use_updated_regime==0 || t<first_period_occbin_update))
|
|
if rescale_prediction_error_covariance
|
|
log_dF = log(det(F./(sig*sig')))+2*sum(log(sig));
|
|
iF = inv(F./(sig*sig'))./(sig*sig');
|
|
rescale_prediction_error_covariance=rescale_prediction_error_covariance0;
|
|
else
|
|
log_dF = log(det(F));
|
|
iF = inv(F);
|
|
end
|
|
lik(s) = log_dF + transpose(v)*iF*v + length(d_index)*log(2*pi);
|
|
if t<first_period_occbin_update
|
|
if Zflag
|
|
K = P*z'*iF;
|
|
if occbin_.status
|
|
P0(:,:,t) = (P-K*z*P);
|
|
end
|
|
|
|
P = T*(P-K*z*P)*transpose(T)+QQ;
|
|
else
|
|
K = P(:,z)*iF;
|
|
if occbin_.status
|
|
P0(:,:,t) = (P-K*P(z,:));
|
|
end
|
|
P = T*(P-K*P(z,:))*transpose(T)+QQ;
|
|
end
|
|
if occbin_.status
|
|
a0(:,t) = (a+K*v);
|
|
vv(d_index,t) = v;
|
|
end
|
|
a = T*(a+K*v)+C;
|
|
if t>=no_more_missing_observations && ~isqvec && ~occbin_.status
|
|
notsteady = max(abs(K(:)-oldK))>riccati_tol;
|
|
oldK = K(:);
|
|
end
|
|
end
|
|
end
|
|
end
|
|
if occbin_.status && t>=first_period_occbin_update
|
|
|
|
occbin_options.opts_simul.waitbar=0;
|
|
if t==1
|
|
if isqvec
|
|
Qt = cat(3,Q,Qvec(:,:,t:t+1));
|
|
end
|
|
a00 = ainit;
|
|
a10 = [a00 a(:,1)];
|
|
P00 = Pinit;
|
|
P10 = P1(:,:,[1 1]);
|
|
data_index0{1}=[];
|
|
data_index0(2)=data_index(1);
|
|
v0(:,2)=vv(:,1);
|
|
Y0(:,2)=Y(:,1);
|
|
Y0(:,1)=nan;
|
|
TT01 = cat(3,T,TT(:,:,1));
|
|
RR01 = cat(3,R,RR(:,:,1));
|
|
CC01 = zeros(size(CC,1),2);
|
|
CC01(:,2) = CC(:,1);
|
|
% insert here kalman update engine
|
|
[ax, a1x, Px, P1x, vx, Tx, Rx, Cx, regx, info, M_, likx] = occbin.kalman_update_engine(a00, a10, P00, P10, t, data_index0, Z, v0, Y0, H, Qt, T0, R0, TT01, RR01, CC01, regimes_(t:t+1), base_regime, d_index, M_, dr, endo_steady_state,exo_steady_state,exo_det_steady_state, options_, occbin_options);
|
|
% [ax, a1x, Px, P1x, vx, Tx, Rx, Cx, regimes_(t:t+2), info, M_, likx] = occbin.kalman_update_algo_1(a00, a10, P00, P10, data_index0, Z, v0, Y0, H, Qt, T0, R0, TT01, RR01, CC01, regimes_(t:t+1), M_, dr, endo_steady_state,exo_steady_state,exo_det_steady_state, options_, occbin_options);
|
|
else
|
|
if isqvec
|
|
Qt = Qvec(:,:,t-1:t+1);
|
|
end
|
|
% insert here kalman update engine
|
|
[ax, a1x, Px, P1x, vx, Tx, Rx, Cx, regx, info, M_, likx] = occbin.kalman_update_engine(a0(:,t-1),a1(:,t-1:t),P0(:,:,t-1),P1(:,:,t-1:t),t,data_index(t-1:t),Z,vv(:,t-1:t),Y(:,t-1:t),H,Qt,T0,R0,TT(:,:,t-1:t),RR(:,:,t-1:t),CC(:,t-1:t),regimes_(t:t+1),base_regime,d_index,M_,dr, endo_steady_state,exo_steady_state,exo_det_steady_state,options_,occbin_options);
|
|
% [ax, a1x, Px, P1x, vx, Tx, Rx, Cx, regimes_(t:t+2), info, M_, likx] = occbin.kalman_update_algo_1(a0(:,t-1),a1(:,t-1:t),P0(:,:,t-1),P1(:,:,t-1:t),data_index(t-1:t),Z,vv(:,t-1:t),Y(:,t-1:t),H,Qt,T0,R0,TT(:,:,t-1:t),RR(:,:,t-1:t),CC(:,t-1:t),regimes_(t:t+1),M_,dr,endo_steady_state,exo_steady_state,exo_det_steady_state,options_,occbin_options);
|
|
end
|
|
if info
|
|
if options_.debug
|
|
fprintf('\nmissing_observations_kalman_filter:PKF failed in period %u with: %s\n', t, get_error_message(info,options_));
|
|
end
|
|
return
|
|
end
|
|
if options_.occbin.likelihood.use_updated_regime
|
|
lik(s) = likx;
|
|
end
|
|
regimes_(t:t+2) = regx;
|
|
a0(:,t) = ax(:,1);
|
|
a1(:,t) = a1x(:,2);
|
|
a = ax(:,2);
|
|
vv(d_index,t) = vx(d_index,2);
|
|
TT(:,:,t:t+1) = Tx;
|
|
RR(:,:,t:t+1) = Rx;
|
|
CC(:,t:t+1) = Cx;
|
|
P0(:,:,t) = Px(:,:,1);
|
|
P1(:,:,t) = P1x(:,:,2);
|
|
P = Px(:,:,2);
|
|
|
|
end
|
|
t = t+1;
|
|
end
|
|
|
|
if F_singular
|
|
error('The variance of the forecast error remains singular until the end of the sample')
|
|
end
|
|
|
|
% Divide by two.
|
|
lik(1:s) = .5*lik(1:s);
|
|
|
|
% Call steady state Kalman filter if needed.
|
|
if t<=last
|
|
[~, lik(s+1:end)] = kalman_filter_ss(Y, t, last, a, T, K, iF, log_dF, Z, pp, Zflag);
|
|
end
|
|
|
|
% Compute minus the log-likelihood.
|
|
if presample>=diffuse_periods
|
|
LIK = sum(lik(1+presample-diffuse_periods:end));
|
|
else
|
|
LIK = sum(lik);
|
|
end
|