Computes the likelihood of a stationnary state space model (steady state univariate kalman filter).
0001 function [LIK,likk,a] = univariate_kalman_filter_ss(Y,start,last,a,P,kalman_tol,T,H,Z,pp,Zflag,analytic_derivation,Da,DT,DYss,DP,DH,D2a,D2T,D2Yss,D2P) 0002 % Computes the likelihood of a stationnary state space model (steady state univariate kalman filter). 0003 0004 %@info: 0005 %! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a} ] =} univariate_kalman_filter_ss (@var{Y}, @var{start}, @var{last}, @var{a}, @var{P}, @var{kalman_tol}, @var{riccati_tol},@var{presample},@var{T},@var{Q},@var{R},@var{H},@var{Z},@var{mm},@var{pp},@var{rr},@var{Zflag},@var{diffuse_periods}) 0006 %! @anchor{univariate_kalman_filter_ss} 0007 %! @sp 1 0008 %! Computes the likelihood of a stationary state space model, given initial condition for the states (mean and variance). 0009 %! @sp 2 0010 %! @strong{Inputs} 0011 %! @sp 1 0012 %! @table @ @var 0013 %! @item Y 0014 %! Matrix (@var{pp}*T) of doubles, data. 0015 %! @item start 0016 %! Integer scalar, first period. 0017 %! @item last 0018 %! Integer scalar, last period (@var{last}-@var{first} has to be inferior to T). 0019 %! @item a 0020 %! Vector (@var{mm}*1) of doubles, initial mean of the state vector. 0021 %! @item P 0022 %! Matrix (@var{mm}*@var{mm}) of doubles, steady state covariance matrix of the state vector. 0023 %! @item kalman_tol 0024 %! Double scalar, tolerance parameter (rcond, inversibility of the covariance matrix of the prediction errors). 0025 %! @item T 0026 %! Matrix (@var{mm}*@var{mm}) of doubles, transition matrix of the state equation. 0027 %! @item H 0028 %! Vector (@var{pp}) of doubles, diagonal of covariance matrix of the measurement errors (corelation among measurement errors is handled by a model transformation). 0029 %! Matrix (@var{pp}*@var{pp}) of doubles, covariance matrix of the measurement errors (if no measurement errors set H as a zero scalar). 0030 %! @item Z 0031 %! Matrix (@var{pp}*@var{mm}) of doubles or vector of integers, matrix relating the states to the observed variables or vector of indices (depending on the value of @var{Zflag}). 0032 %! @item pp 0033 %! Integer scalar, number of observed variables. 0034 %! @item Zflag 0035 %! Integer scalar, equal to 0 if Z is a vector of indices targeting the obseved variables in the state vector, equal to 1 if Z is a @var{pp}*@var{mm} matrix. 0036 %! @end table 0037 %! @sp 2 0038 %! @strong{Outputs} 0039 %! @sp 1 0040 %! @table @ @var 0041 %! @item LIK 0042 %! Double scalar, value of (minus) the likelihood. 0043 %! @item likk 0044 %! Column vector of doubles, values of the density of each observation. 0045 %! @item a 0046 %! Vector (@var{mm}*1) of doubles, mean of the state vector at the end of the (sub)sample. 0047 %! @end table 0048 %! @sp 2 0049 %! @strong{This function is called by:} 0050 %! @sp 1 0051 %! @ref{univariate_kalman_filter} 0052 %! @sp 2 0053 %! @strong{This function calls:} 0054 %! @sp 1 0055 %! @end deftypefn 0056 %@eod: 0057 0058 % Copyright (C) 2011 Dynare Team 0059 % 0060 % This file is part of Dynare. 0061 % 0062 % Dynare is free software: you can redistribute it and/or modify 0063 % it under the terms of the GNU General Public License as published by 0064 % the Free Software Foundation, either version 3 of the License, or 0065 % (at your option) any later version. 0066 % 0067 % Dynare is distributed in the hope that it will be useful, 0068 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0069 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0070 % GNU General Public License for more details. 0071 % 0072 % You should have received a copy of the GNU General Public License 0073 % along with Dynare. If not, see <http://www.gnu.org/licenses/>. 0074 0075 % AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT fr 0076 0077 % Get sample size. 0078 smpl = last-start+1; 0079 0080 % Initialize some variables. 0081 t = start; % Initialization of the time index. 0082 likk = zeros(smpl,1); % Initialization of the vector gathering the densities. 0083 LIK = Inf; % Default value of the log likelihood. 0084 l2pi = log(2*pi); 0085 0086 if nargin<12 0087 analytic_derivation = 0; 0088 end 0089 0090 if analytic_derivation == 0, 0091 DLIK=[]; 0092 Hess=[]; 0093 else 0094 k = size(DT,3); % number of structural parameters 0095 DLIK = zeros(k,1); % Initialization of the score. 0096 if analytic_derivation==2, 0097 Hess = zeros(k,k); % Initialization of the Hessian 0098 else 0099 Hess=[]; 0100 end 0101 end 0102 0103 % Steady state kalman filter. 0104 while t<=last 0105 s = t-start+1; 0106 PP = P; 0107 if analytic_derivation, 0108 DPP = DP; 0109 if analytic_derivation==2, 0110 D2PP = D2P; 0111 end 0112 end 0113 for i=1:pp 0114 if Zflag 0115 prediction_error = Y(i,t) - Z(i,:)*a; 0116 PPZ = PP*Z(i,:)'; 0117 Fi = Z(i,:)*PPZ + H(i); 0118 else 0119 prediction_error = Y(i,t) - a(Z(i)); 0120 PPZ = PP(:,Z(i)); 0121 Fi = PPZ(Z(i)) + H(i); 0122 end 0123 if Fi>kalman_tol 0124 Ki = PPZ/Fi; 0125 a = a + Ki*prediction_error; 0126 PP = PP - PPZ*Ki'; 0127 likk(s) = likk(s) + log(Fi) + prediction_error*prediction_error/Fi + l2pi; 0128 if analytic_derivation, 0129 if analytic_derivation==2, 0130 [Da,DPP,DLIKt,D2a,D2PP, Hesst] = univariate_computeDLIK(k,i,Z(i,:),Zflag,prediction_error,Ki,PPZ,Fi,Da,DYss,DPP,DH(i,:),0,D2a,D2Yss,D2PP); 0131 else 0132 [Da,DPP,DLIKt] = univariate_computeDLIK(k,i,Z(i,:),Zflag,prediction_error,Ki,PPZ,Fi,Da,DYss,DPP,DH(i,:),0); 0133 end 0134 DLIK = DLIK + DLIKt; 0135 if analytic_derivation==2, 0136 Hess = Hess + Hesst; 0137 end 0138 end 0139 end 0140 end 0141 if analytic_derivation, 0142 if analytic_derivation==2, 0143 [Da,junk,D2a] = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0,D2a,D2P,D2T); 0144 else 0145 Da = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0); 0146 end 0147 end 0148 a = T*a; 0149 t = t+1; 0150 end 0151 0152 likk = .5*likk; 0153 0154 LIK = sum(likk); 0155 if analytic_derivation==2, 0156 LIK={LIK,DLIK,Hess}; 0157 end 0158 if analytic_derivation==1, 0159 LIK={LIK,DLIK}; 0160 end