179 lines
6.3 KiB
Matlab
179 lines
6.3 KiB
Matlab
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)
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% Computes the likelihood of a stationnary state space model (steady state univariate kalman filter).
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%@info:
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%! @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})
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%! @anchor{univariate_kalman_filter_ss}
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%! @sp 1
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%! Computes the likelihood of a stationary state space model, given initial condition for the states (mean and variance).
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item Y
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%! Matrix (@var{pp}*T) of doubles, data.
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%! @item start
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%! Integer scalar, first period.
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%! @item last
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%! Integer scalar, last period (@var{last}-@var{first} has to be inferior to T).
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%! @item a
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%! Vector (@var{mm}*1) of doubles, initial mean of the state vector.
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%! @item P
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%! Matrix (@var{mm}*@var{mm}) of doubles, steady state covariance matrix of the state vector.
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%! @item kalman_tol
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%! Double scalar, tolerance parameter (rcond, inversibility of the covariance matrix of the prediction errors).
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%! @item T
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%! Matrix (@var{mm}*@var{mm}) of doubles, transition matrix of the state equation.
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%! @item H
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%! Vector (@var{pp}) of doubles, diagonal of covariance matrix of the measurement errors (corelation among measurement errors is handled by a model transformation).
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%! Matrix (@var{pp}*@var{pp}) of doubles, covariance matrix of the measurement errors (if no measurement errors set H as a zero scalar).
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%! @item Z
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%! 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}).
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%! @item pp
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%! Integer scalar, number of observed variables.
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%! @item Zflag
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%! 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.
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%! @end table
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%! @sp 2
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item LIK
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%! Double scalar, value of (minus) the likelihood.
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%! @item likk
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%! Column vector of doubles, values of the density of each observation.
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%! @item a
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%! Vector (@var{mm}*1) of doubles, mean of the state vector at the end of the (sub)sample.
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%! @end table
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%! @sp 2
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%! @strong{This function is called by:}
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%! @sp 1
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%! @ref{univariate_kalman_filter}
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%! @sp 2
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%! @strong{This function calls:}
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%! @sp 1
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%! @end deftypefn
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%@eod:
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%
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% Algorithm: See univariate_kalman_filter.m
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% Copyright © 2011-2017 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 <https://www.gnu.org/licenses/>.
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% AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT fr
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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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likk = zeros(smpl,pp); % 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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asy_hess=0;
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if nargin<12
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analytic_derivation = 0;
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end
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if analytic_derivation == 0
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DLIK=[];
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Hess=[];
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else
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k = size(DT,3); % number of structural parameters
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DLIK = zeros(k,1); % Initialization of the score.
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dlikk = zeros(smpl,k);
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if analytic_derivation==2
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Hess = zeros(k,k); % Initialization of the Hessian
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else
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asy_hess=D2a;
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if asy_hess
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Hess = zeros(k,k); % Initialization of the Hessian
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else
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Hess=[];
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end
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end
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end
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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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if analytic_derivation
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DPP = DP;
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if analytic_derivation==2
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D2PP = D2P;
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end
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end
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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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PPZ = PP*Z(i,:)';
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Fi = Z(i,:)*PPZ + H(i);
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else
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prediction_error = Y(i,t) - a(Z(i));
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PPZ = PP(:,Z(i));
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Fi = PPZ(Z(i)) + H(i);
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end
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if Fi>kalman_tol
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Ki = PPZ/Fi;
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a = a + Ki*prediction_error;
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PP = PP - PPZ*Ki';
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likk(s,i) = log(Fi) + prediction_error*prediction_error/Fi + l2pi;
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if analytic_derivation
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if analytic_derivation==2
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[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);
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else
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[Da,DPP,DLIKt,Hesst] = univariate_computeDLIK(k,i,Z(i,:),Zflag,prediction_error,Ki,PPZ,Fi,Da,DYss,DPP,DH(i,:),0);
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end
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DLIK = DLIK + DLIKt;
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if analytic_derivation==2 || asy_hess
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Hess = Hess + Hesst;
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end
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dlikk(s,:)=dlikk(s,:)+DLIKt';
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end
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else
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% do nothing as a_{t,i+1}=a_{t,i} and P_{t,i+1}=P_{t,i}, see
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% p. 157, DK (2012)
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end
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end
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if analytic_derivation
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if analytic_derivation==2
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[Da,~,D2a] = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0,D2a,D2P,D2T);
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else
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Da = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0);
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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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likk = .5*likk;
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LIK = sum(sum(likk));
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if analytic_derivation
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dlikk = dlikk/2;
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DLIK = DLIK/2;
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likk = {likk, dlikk};
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end
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if analytic_derivation==2 || asy_hess
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% Hess = (Hess + Hess')/2;
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Hess = -Hess/2;
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LIK={LIK,DLIK,Hess};
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elseif analytic_derivation==1
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LIK={LIK,DLIK};
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end |