168 lines
6.0 KiB
Matlab
168 lines
6.0 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)
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% Computes the likelihood of a state space model in the case with missing observations.
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%
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% INPUTS
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% data_index [cell] 1*smpl cell of column vectors of indices.
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% number_of_observations [integer] scalar.
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% no_more_missing_observations [integer] scalar.
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% Y [double] pp*smpl matrix of data.
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% start [integer] scalar, index of the first observation.
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% last [integer] scalar, index of the last observation.
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% a [double] pp*1 vector, initial level of the state vector.
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% P [double] pp*pp matrix, covariance matrix of the initial state vector.
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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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% presample [integer] scalar, presampling if strictly positive.
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% T [double] mm*mm transition matrix of the state equation.
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% Q [double] rr*rr covariance matrix of the structural innovations.
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% R [double] mm*rr matrix, mapping structural innovations to state variables.
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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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% Z [integer] pp*1 vector of indices for the observed variables.
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% mm [integer] scalar, dimension of the state vector.
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% pp [integer] scalar, number of observed variables.
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% rr [integer] scalar, number of structural innovations.
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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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% a [double] mm*1 vector, estimated level of the states.
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% P [double] mm*mm matrix, covariance matrix of the states.
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%
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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) 2004-2017 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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% Set defaults
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if nargin<20
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Zflag = 0;
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diffuse_periods = 0;
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end
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if nargin<21
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diffuse_periods = 0;
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end
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if isempty(Zflag)
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Zflag = 0;
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end
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if isempty(diffuse_periods)
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diffuse_periods = 0;
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end
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if isequal(H,0)
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H = zeros(pp,pp);
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end
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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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dF = 1;
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QQ = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
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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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oldK = Inf;
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notsteady = 1;
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F_singular = true;
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s = 0;
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while notsteady && t<=last
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s = t-start+1;
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d_index = data_index{t};
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if isempty(d_index)
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a = T*a;
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P = T*P*transpose(T)+QQ;
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else
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% Compute the prediction error and its variance
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if Zflag
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z = Z(d_index,:);
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v = Y(d_index,t)-z*a;
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F = z*P*z' + H(d_index,d_index);
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else
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z = Z(d_index);
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v = Y(d_index,t) - a(z);
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F = P(z,z) + H(d_index,d_index);
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end
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badly_conditioned_F = false;
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if rescale_prediction_error_covariance
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sig=sqrt(diag(F));
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if any(diag(F)<kalman_tol) || rcond(F./(sig*sig'))<kalman_tol
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badly_conditioned_F = true;
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end
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else
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if rcond(F)<kalman_tol
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badly_conditioned_F = true;
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end
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end
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if badly_conditioned_F
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if ~all(abs(F(:))<kalman_tol)
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% Use univariate filter.
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return
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else
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% Pathological case, discard draw
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return
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end
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else
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F_singular = false;
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if rescale_prediction_error_covariance
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log_dF = log(det(F./(sig*sig')))+2*sum(log(sig));
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iF = inv(F./(sig*sig'))./(sig*sig');
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else
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log_dF = log(det(F));
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iF = inv(F);
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end
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lik(s) = log_dF + transpose(v)*iF*v + length(d_index)*log(2*pi);
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if Zflag
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K = P*z'*iF;
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P = T*(P-K*z*P)*transpose(T)+QQ;
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else
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K = P(:,z)*iF;
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P = T*(P-K*P(z,:))*transpose(T)+QQ;
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end
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a = T*(a+K*v);
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if t>=no_more_missing_observations
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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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end
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t = t+1;
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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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% Divide by two.
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lik(1:s) = .5*lik(1:s);
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% Call steady state Kalman filter if needed.
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if t<=last
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[tmp, lik(s+1:end)] = kalman_filter_ss(Y, t, last, a, T, K, iF, log_dF, Z, pp, Zflag);
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end
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% Compute minus the log-likelihood.
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if presample>=diffuse_periods
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LIK = sum(lik(1+presample-diffuse_periods:end));
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else
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LIK = sum(lik);
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end |