70 lines
2.9 KiB
Matlab
70 lines
2.9 KiB
Matlab
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function [LIK, lik, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,dF,Z,pp,Zflag)
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% Computes the likelihood of a stationnary state space model (steady state kalman filter).
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%
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% INPUTS
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% Y [double] pp*smpl matrix of data.
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% start [integer] scalar, index of the first observation (column of Y).
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% last [integer] scalar, index of the last observation (column of Y).
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% a [double] mm*1 vector, initial level of the state vector.
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% P [double] mm*mm matrix, covariance matrix of the initial state vector.
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% T [double] mm*mm transition matrix of the state equation.
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% K [double] mm*pp matrix, steady state kalman gain.
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% iF [double] pp*pp matrix, inverse of the steady state covariance matrix of the predicted errors.
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% dF [double] scalar, determinant of the steady state covariance matrix of the predicted errors.
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% Z [integer] pp*1 vector of indices for the observed variables, if Zflag=0.
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% pp [integer] scalar, number of observed variables.
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%
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%
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% OUTPUTS
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% LIK [double] scalar, minus log likelihood.
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% lik [double] (last-start+1)*1 vector, density of each observation.
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% a [double] mm*1 vector, estimate of the state vector.
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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) 2011 Dynare Team
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% stephane DOT adjemian AT ens DOT fr
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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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% Get sample size.
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smpl = last-start+1;
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% Initialize some variables.
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t = start; % 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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while t <= last
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if Zflag
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v = Y(:,t)-Z*a;
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else
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v = Y(:,t)-a(Z);
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end
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a = T*(a+K*v);
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lik(t-start+1) = transpose(v)*iF*v;
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t = t+1;
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end
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% Adding constant determinant of F (prediction error covariance matrix)
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lik = lik + log(dF);
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% Add log-likelihhod constants and divide by two
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lik = .5*(lik + pp*log(2*pi));
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% Sum the observation's densities (minus the likelihood)
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LIK = sum(lik);
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