80 lines
2.9 KiB
Matlab
80 lines
2.9 KiB
Matlab
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function [LIK, lik,a] = univariate_kalman_filter_ss(Y,start,last,a,P,kalman_tol,T,H,Z,pp,Zflag)
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% Computes the likelihood of a stationnary state space model (steady state univariate 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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% Z [integer] pp*1 vector of indices for the observed variables.
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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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l2pi = log(2*pi);
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% Steady state kalman filter.
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while t<=last
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s = t-start+1;
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PP = P;
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for i=1:pp
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if Zflag
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prediction_error = Y(i,t) - Z(i,:)*a;
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Fi = Z(i,:)*PP*Z(i,:)' + H(i,i);
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else
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prediction_error = Y(i,t) - a(Z(i));
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Fi = PP(Z(i),Z(i)) + H(i,i);
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end
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if Fi>kalman_tol
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if Zflag
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Ki = PP*Z(i,:)'/Fi;
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else
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Ki = PP(:,Z(i))/Fi;
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end
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a = a + Ki*prediction_error;
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PP = PP - (Fi*Ki)*transpose(Ki);
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lik(s) = lik(s) + log(Fi) + prediction_error*prediction_error/Fi + l2pi;
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end
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end
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a = T*a;
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t = t+1;
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end
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lik = .5*lik;
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LIK = sum(lik);
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