100 lines
4.0 KiB
Matlab
100 lines
4.0 KiB
Matlab
function [LIK, lik] = kalman_filter(T,R,Q,H,P,Y,start,mf,kalman_tol,riccati_tol)
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% Computes the likelihood of a stationnary state space model.
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%
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% INPUTS
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% T [double] mm*mm transition matrix of the state equation.
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% R [double] mm*rr matrix, mapping structural innovations to state variables.
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% Q [double] rr*rr covariance matrix of the structural innovations.
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% H [double] pp*pp (or 1*1 =0 if no measurement error) covariance matrix of the measurement errors.
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% P [double] mm*mm variance-covariance matrix with stationary variables
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% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
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% start [integer] scalar, likelihood evaluation starts at 'start'.
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% mf [integer] pp*1 vector of indices.
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% kalman_tol [double] scalar, tolerance parameter (rcond).
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% riccati_tol [double] scalar, tolerance parameter (riccati iteration).
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%
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% OUTPUTS
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% LIK [double] scalar, MINUS loglikelihood
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% lik [double] vector, density of observations in each period.
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%
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% REFERENCES
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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%
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2004-2010 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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smpl = size(Y,2); % Sample size.
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mm = size(T,2); % Number of state variables.
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pp = size(Y,1); % Maximum number of observed variables.
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a = zeros(mm,1); % State vector.
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dF = 1; % det(F).
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QQ = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
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t = 0; % Initialization of the time index.
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lik = zeros(smpl,1); % Initialization of the vector gathering the densities.
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LIK = Inf; % Default value of the log likelihood.
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oldK = Inf;
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notsteady = 1; % Steady state flag.
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F_singular = 1;
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while notsteady & t<smpl
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t = t+1;
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v = Y(:,t)-a(mf);
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F = P(mf,mf) + H;
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if rcond(F) < kalman_tol
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if ~all(abs(F(:))<kalman_tol)
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return
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else
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a = T*a;
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P = T*P*transpose(T)+QQ;
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end
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else
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F_singular = 0;
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dF = det(F);
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iF = inv(F);
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lik(t) = log(dF)+transpose(v)*iF*v;
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K = P(:,mf)*iF;
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a = T*(a+K*v);
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P = T*(P-K*P(mf,:))*transpose(T)+QQ;
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notsteady = max(abs(K(:)-oldK)) > riccati_tol;
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oldK = K(:);
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end
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end
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if F_singular
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error('The variance of the forecast error remains singular until the end of the sample')
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end
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if t < smpl
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t0 = t+1;
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while t < smpl
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t = t+1;
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v = Y(:,t)-a(mf);
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a = T*(a+K*v);
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lik(t) = transpose(v)*iF*v;
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end
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lik(t0:smpl) = lik(t0:smpl) + log(dF);
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end
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% adding log-likelihhod constants
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lik = (lik + pp*log(2*pi))/2;
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LIK = sum(lik(start:end)); % Minus the log-likelihood. |