Added texinfo header.
Stéphane Adjemian (Charybdis)
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function [LIK, lik, a, Pstar, llik] = univariate_kalman_filter_d(data_index, number_of_observations, no_more_missing_observations, ...
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Y, start, last, a, Pinf, Pstar, kalman_tol, riccati_tol, presample, ...
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T,R,Q,H,Z,mm,pp,rr)
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% Computes the diffuse likelihood of a stationnary state space model (univariate approach).
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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 (detrended) data, where pp is the number of observed variables.
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% start [integer] scalar, first observation.
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% last [integer] scalar, last observation.
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% a [double] mm*1 vector, levels of the state variables.
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% Pinf [double] mm*mm matrix used to initialize the covariance matrix of the state vector.
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% Pstar [double] mm*mm matrix used to initialize the covariance matrix of the 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 matrix, transition matrix in the state equations.
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% R [double] mm*rr matrix relating the structural innovations to the state vector.
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% Q [double] rr*rr covariance matrix of the structural innovations.
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% H [double] pp*pp covariance matrix of the measurement errors (if H is equal to zero (scalar) there is no measurement error).
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% Z [double] pp*mm matrix, selection matrix or pp linear independant combinations of the state vector.
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% mm [integer] scalar, number of state variables.
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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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% dLIK [double] scalar, minus loglikelihood
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% dlik [double] d*1 vector, log density of each vector of observations (where d is the number of periods of the diffuse filter).
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% a [double] mm*1 vector, current estimate of the state vector.
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% Pstar [double] mm*mm matrix, covariance matrix of the state vector.
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% llik [double] d*pp matrix used by DsgeLikelihood_hh.
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%
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% REFERENCES
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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%
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% NOTES
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% The vector "llik" is used to evaluate the jacobian of the likelihood.
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function [dLIK, dlikk, a, Pstar, llik] = univariate_kalman_filter_d(data_index, number_of_observations, no_more_missing_observations, Y, start, last, a, Pinf, Pstar, kalman_tol, riccati_tol, presample, T, R, Q, H, Z, mm, pp, rr)
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% Computes the likelihood of a state space model (initialization with diffuse steps, univariate approach).
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%@info:
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%! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a},@var{Pstar}, @var{llik} ] =} univariate_kalman_filter_d (@var{data_index}, @var{number_of_observations},@var{no_more_missing_observations}, @var{Y}, @var{start}, @var{last}, @var{a}, @var{Pinf}, @var{Pstar}, @var{kalman_tol}, @var{riccati_tol},@var{presample},@var{T},@var{R},@var{Q},@var{H},@var{Z},@var{mm},@var{pp},@var{rr})
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%! @anchor{univariate_kalman_filter_d}
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%! @sp 1
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%! Computes the likelihood of a state space model (initialization with diffuse steps, univariate approach).
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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 data_index
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%! Matlab's cell, 1*T cell of column vectors of indices (in the vector of observed variables).
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%! @item number_of_observations
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%! Integer scalar, effective number of observations.
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%! @item no_more_missing_observations
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%! Integer scalar, date after which there is no more missing observation (it is then possible to switch to the steady state kalman filter).
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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 Pinf
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%! Matrix (@var{mm}*@var{mm}) of doubles, initial covariance matrix of the state vector (non stationary part).
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%! @item Pstar
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%! Matrix (@var{mm}*@var{mm}) of doubles, initial covariance matrix of the state vector (stationary part).
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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 riccati_tol
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%! Double scalar, tolerance parameter (iteration over the Riccati equation).
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%! @item presample
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%! Integer scalar, presampling if strictly positive (number of initial iterations to be discarded when evaluating the likelihood).
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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 R
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%! Matrix (@var{mm}*@var{rr}) of doubles, second matrix of the state equation relating the structural innovations to the state variables.
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%! @item Q
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%! Matrix (@var{rr}*@var{rr}) of doubles, covariance matrix of the structural innovations (noise in the state equation).
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%! @item H
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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, matrix relating the states to the observed variables.
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%! @item mm
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%! Integer scalar, number of state variables.
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%! @item pp
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%! Integer scalar, number of observed variables.
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%! @item rr
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%! Integer scalar, number of structural innovations.
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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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%! @item diffuse_periods
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%! Integer scalar, number of diffuse filter periods in the initialization step.
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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 dLIK
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%! Double scalar, value of (minus) the likelihood for the first d observations.
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%! @item likk
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%! Column vector (d*1) of doubles, values of the density of each (fist) observations.
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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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%! @item Pstar
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%! Matrix (@var{mm}*@var{mm}) of doubles, covariance of the state vector at the end of the subsample.
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%! @item llik
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%! Matrix of doubles (d*@var{pp}) used by @ref{DsgeLikelihood_hh}
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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{DsgeLikelihood}, @ref{DsgeLikelihood_hh}
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%! @sp 2
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%! @strong{This function calls:}
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%! @sp 1
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%! @ref{univariate_kalman_filter_ss}
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%! @end deftypefn
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%@eod:
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% Copyright (C) 2004-2011 Dynare Team
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%
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@ -64,7 +105,7 @@ smpl = last-start+1;
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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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dlik = zeros(smpl,1); % Initialization of the vector gathering the densities.
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dlikk= zeros(smpl,1); % Initialization of the vector gathering the densities.
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dLIK = Inf; % Default value of the log likelihood.
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oldK = Inf;
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llik = NaN(smpl,pp);
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@ -88,10 +129,10 @@ while newRank && (t<=last)
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Pstar = Pstar + Kinf*(Kinf_Finf'*(Fstar/Finf)) - Kstar*Kinf_Finf' - Kinf_Finf*Kstar';
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Pinf = Pinf - Kinf*Kinf_Finf';
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llik(s,d_index(i)) = log(Finf) + l2pi;
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dlik(s) = dlik(s) + llik(s,d_index(i));
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dlikk(s) = dlikk(s) + llik(s,d_index(i));
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elseif Fstar>kalman_tol
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llik(s,d_index(i)) = log(Fstar) + prediction_error*prediction_error/Fstar + l2pi;
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dlik(s) = dlik(s) + llik(s,d_index(i));
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dlikk(s) = dlikk(s) + llik(s,d_index(i));
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a = a+Kstar*(prediction_error/Fstar);
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Pstar = Pstar-Kstar*(Kstar'/Fstar);
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end
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@ -108,7 +149,7 @@ while newRank && (t<=last)
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newRank = rank(Pinf,kalman_tol);
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end
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if oldRank ~= newRank
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disp('univariate_diffuse_kalman_filter:: T does influence the rank of Pinf!')
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disp('univariate_diffuse_kalman_filter:: T does influence the rank of Pinf!')
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end
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t = t+1;
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end
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@ -120,19 +161,19 @@ if (t>last)
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end
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% Divide by two.
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dlik = .5*dlik(1:s);
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llik = .5*llik(1:s,:);
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dlikk = .5*dlikk(1:s);
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llik = .5*llik(1:s,:);
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if presample
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if presample
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if presample>=length(dlik)
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dLIK = 0;
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dlik = [];
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dlikk= [];
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llik = [];
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else
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dlik = dlik(1+presample:end);
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dlikk= dlikk(1+presample:end);
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llik = llik(1+presample:end,:);
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dLIK = sum(dlik);% Minus the log-likelihood (for the initial periods).
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dLIK = sum(dlikk);% Minus the log-likelihood (for the initial periods).
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end
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else
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dLIK = sum(dlik);
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dLIK = sum(dlikk);
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end
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