Added texinfo header.
Stéphane Adjemian (Charybdis)
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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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%@info:
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%! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a},@var{P} ] =} DsgeLikelihood (@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{kalman_filter}
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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), the steady state kalman gain and the steady state inveverted covariance matrix of the prediction errors.
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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 (mm*1) of doubles, initial mean of the state vector.
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%! @item T
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%! Matrix (mm*mm) of doubles, transition matrix of the state equation.
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%! @item K
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%! Matrix (mm*@var{pp}) of doubles, steady state kalman gain.
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%! @item iF
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%! Matrix (@var{pp}*@var{pp}) of doubles, inverse of the steady state covariance matrix of the prediction errors.
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%! @item dF
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%! Double scalar, determinant of the steady state covariance matrix of teh prediction errors.
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%! @item Z
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%! Matrix (@var{pp}*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 (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{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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% Copyright (C) 2011 Dynare Team
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% stephane DOT adjemian AT ens DOT fr
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%
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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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@ -41,6 +71,8 @@ function [LIK, lik, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,dF,Z,pp,Zflag)
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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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% 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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@ -66,5 +98,5 @@ 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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% Sum the observation's densities (minus the likelihood)
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LIK = sum(lik);
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