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v4.1: Added a new m file for the univariate kalman filter allowing for missing observations and 

correlated measurement errors. Tests show that there is a "significant" discrepancy between the 
univariate filter and the standard filter in presence of correlated measurement errors... 

 


git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@2185 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
adjemian 2008-10-21 15:29:33 +00:00
parent 1792d54f59
commit 42bdc2726c
2 changed files with 214 additions and 95 deletions
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190
matlab/kalman/likelihood/univariate_kalman_filter.m
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@ -1,96 +1,96 @@
function [LIK, lik] = univariate_kalman_filter(T,R,Q,H,P,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations)
% Computes the likelihood of a stationnary state space model (univariate approach).
%
% INPUTS
% T [double] mm*mm transition matrix of the state equation.
% R [double] mm*rr matrix, mapping structural innovations to state variables.
% Q [double] rr*rr covariance matrix of the structural innovations.
% H [double] pp*1 (zeros(pp,1) if no measurement errors) variances of the measurement errors.
% P [double] mm*mm variance-covariance matrix with stationary variables
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
% start [integer] scalar, likelihood evaluation starts at 'start'.
% mf [integer] pp*1 vector of indices.
% kalman_tol [double] scalar, tolerance parameter (rcond).
% riccati_tol [double] scalar, tolerance parameter (riccati iteration).
% data_index [cell] 1*smpl cell of column vectors of indices.
% number_of_observations [integer] scalar.
% no_more_missing_observations [integer] scalar.
%
% OUTPUTS
% LIK [double] scalar, likelihood
% lik [double] vector, density of observations in each period.
%
% REFERENCES
% 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).
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2004-2008 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/>.
pp = size(Y,1); % Number of observed variables
mm = size(T,1); % Number of variables in the state vector.
smpl = size(Y,2); % Number of periods in the dataset.
a = zeros(mm,1); % Initial condition of the state vector.
QQ = R*Q*transpose(R);
t = 0;
lik = zeros(smpl+1,1);
lik(smpl+1) = number_of_observations*log(2*pi); % the constant of minus two times the log-likelihood
notsteady = 1;
while notsteady && t<smpl
t = t+1;
MF = mf(data_index{t});
oldP = P;
for i=1:length(MF)
prediction_error = Y(data_index{t}(i),t) - a(MF(i));
Fi = P(MF(i),MF(i)) + H(data_index{t}(i));
if Fi > kalman_tol
Ki = P(:,MF(i))/Fi;
a = a + Ki*prediction_error;
P = P - (Fi*Ki)*transpose(Ki);
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
end
end
a = T*a;
P = T*P*transpose(T) + QQ;
if t>no_more_missing_observations
notsteady = max(max(abs(P-oldP)))>riccati_tol;
end
end
% Steady state kalman filter.
while t < smpl
PP = P;
t = t+1;
for i=1:pp
prediction_error = Y(i,t) - a(mf(i));
Fi = PP(mf(i),mf(i)) + H(i);
if Fi > kalman_tol
Ki = PP(:,mf(i))/Fi;
a = a + Ki*prediction_error;
PP = PP - (Fi*Ki)*transpose(Ki);
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
end
end
a = T*a;
end
function [LIK, lik] = univariate_kalman_filter(T,R,Q,H,P,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations)
% Computes the likelihood of a stationnary state space model (univariate approach).
%
% INPUTS
% T [double] mm*mm transition matrix of the state equation.
% R [double] mm*rr matrix, mapping structural innovations to state variables.
% Q [double] rr*rr covariance matrix of the structural innovations.
% H [double] pp*1 (zeros(pp,1) if no measurement errors) variances of the measurement errors.
% P [double] mm*mm variance-covariance matrix with stationary variables
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
% start [integer] scalar, likelihood evaluation starts at 'start'.
% mf [integer] pp*1 vector of indices.
% kalman_tol [double] scalar, tolerance parameter (rcond).
% riccati_tol [double] scalar, tolerance parameter (riccati iteration).
% data_index [cell] 1*smpl cell of column vectors of indices.
% number_of_observations [integer] scalar.
% no_more_missing_observations [integer] scalar.
%
% OUTPUTS
% LIK [double] scalar, likelihood
% lik [double] vector, density of observations in each period.
%
% REFERENCES
% 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).
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2004-2008 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/>.
pp = size(Y,1); % Number of observed variables
mm = size(T,1); % Number of variables in the state vector.
smpl = size(Y,2); % Number of periods in the dataset.
a = zeros(mm,1); % Initial condition of the state vector.
QQ = R*Q*transpose(R);
t = 0;
lik = zeros(smpl+1,1);
lik(smpl+1) = number_of_observations*log(2*pi); % the constant of minus two times the log-likelihood
notsteady = 1;
while notsteady && t<smpl
t = t+1;
MF = mf(data_index{t});
oldP = P;
for i=1:length(MF)
prediction_error = Y(data_index{t}(i),t) - a(MF(i));
Fi = P(MF(i),MF(i)) + H(data_index{t}(i));
if Fi > kalman_tol
Ki = P(:,MF(i))/Fi;
a = a + Ki*prediction_error;
P = P - (Fi*Ki)*transpose(Ki);
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
end
end
a = T*a;
P = T*P*transpose(T) + QQ;
if t>no_more_missing_observations
notsteady = max(max(abs(P-oldP)))>riccati_tol;
end
end
% Steady state kalman filter.
while t < smpl
PP = P;
t = t+1;
for i=1:pp
prediction_error = Y(i,t) - a(mf(i));
Fi = PP(mf(i),mf(i)) + H(i);
if Fi > kalman_tol
Ki = PP(:,mf(i))/Fi;
a = a + Ki*prediction_error;
PP = PP - (Fi*Ki)*transpose(Ki);
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
end
end
a = T*a;
end
LIK = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl);

119
matlab/kalman/likelihood/univariate_kalman_filter_corr.m Normal file
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@ -0,0 +1,119 @@
function [LIK, lik] = ...
univariate_kalman_filter_corr(T,R,Q,H,P,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations)
% Computes the likelihood of a stationnary state space model (univariate
% approach + correlated measurement errors).
%
% INPUTS
% T [double] mm*mm transition matrix of the state equation.
% R [double] mm*rr matrix, mapping structural innovations to state variables.
% Q [double] rr*rr covariance matrix of the structural innovations.
% H [double] pp*pp covariance matrix of the measurement error.
% P [double] mm*mm variance-covariance matrix with stationary variables
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
% start [integer] scalar, likelihood evaluation starts at 'start'.
% Z [integer] pp*mm selection matrix.
% kalman_tol [double] scalar, tolerance parameter (rcond).
% riccati_tol [double] scalar, tolerance parameter (riccati iteration).
% data_index [cell] 1*smpl cell of column vectors of indices.
% number_of_observations [integer] scalar.
% no_more_missing_observations [integer] scalar.
%
% OUTPUTS
% LIK [double] scalar, likelihood
% lik [double] vector, density of observations in each period.
%
% REFERENCES
% 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).
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2004-2008 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/>.
pp = size(Y,1); % Number of observed variables
mm = size(T,1); % Number of variables in the state vector.
rr = size(R,2); % Number of structural innovations.
smpl = size(Y,2); % Number of periods in the dataset.
a = zeros(mm+pp,1); % Initial condition of the state vector.
t = 0;
lik = zeros(smpl+1,1);
lik(smpl+1) = number_of_observations*log(2*pi); % the constant of minus two times the log-likelihood
notsteady = 1;
TT = zeros(mm+pp);
TT(1:mm,1:mm) = T;
QQ = zeros(rr+pp);
QQ(1:rr,1:rr) = Q;
QQ(rr+1:end,rr+1:end) = H;
RR = zeros(mm+pp,rr+pp);
RR(1:mm,1:rr) = R;
RR(mm+1:end,rr+1:end) = eye(pp);
PP = zeros(mm+pp);
PP(1:mm,1:mm) = P;
PP(mm+1:end,mm+1:end) = H;
QQQQ = zeros(mm+pp);
RQR = R*Q*R';
QQQQ(1:mm,1:mm) = RQR;
QQQQ(mm+1:end,mm+1:end) = H;
while notsteady && t<smpl
t = t+1;
MF = mf(data_index{t});
oldPP = PP;
for i=1:length(MF)
prediction_error = Y(data_index{t}(i),t) - a(MF(i)) - a( mm+i );
Fi = PP(MF(i),MF(i)) + PP(mm+i,mm+i);
if Fi > kalman_tol
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
Ki = sum(PP(:,[MF(i) mm+i]),2)/Fi;
a = a + Ki*prediction_error;
PP = PP - (Ki*Fi)*transpose(Ki);
end
end
a(1:mm) = T*a(1:mm);
a(mm+1:end) = zeros(pp,1);
PP(1:mm,1:mm) = T*PP(1:mm,1:mm)*transpose(T) + RQR;
PP(mm+1:end,1:mm) = zeros(pp,mm);
PP(1:mm,mm+1:end) = zeros(mm,pp);
PP(mm+1:end,mm+1:end) = H;
if t>no_more_missing_observations
notsteady = max(max(abs(PP-oldPP)))>riccati_tol;
end
end
% Steady state kalman filter.
while t < smpl
PPPP = PP;
t = t+1;
for i=1:pp
prediction_error = Y(i,t) - a(mf(i)) - a(mm+i);
Fi = PPPP(mf(i),mf(i)) + PPPP(mm+i,mm+i);
if Fi > kalman_tol
Ki = ( PPPP(:,mf(i)) + PPPP(:,mm+i) )/Fi;
a = a + Ki*prediction_error;
PPPP = PPPP - (Fi*Ki)*transpose(Ki);
lik(t) = lik(t) + log(Fi) + prediction_error*prediction_error/Fi;
end
end
a(1:mm) = T*a(1:mm);
a(mm+1:end) = zeros(pp,1);
end
LIK = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl);