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function DynareOutput = simul_backward_nonlinear_model ( sample_size,DynareOptions,DynareModel,DynareOutput)
%@info:
%! @deftypefn {Function File} {@var{DynareOutput} =} simul_backward_nonlinear_model (@var{sample_size},@var{DynareOptions}, @var{DynareModel}, @var{DynareOutput})
%! @anchor{@simul_backward_nonlinear_model}
%! @sp 1
%! Simulates a stochastic non linear backward looking model with arbitrary precision (a deterministic solver is used).
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item sample_size
%! Scalar integer, size of the sample to be generated.
%! @item DynareOptions
%! Matlab/Octave structure (Options used by Dynare).
%! @item DynareDynareModel
%! Matlab/Octave structure (Description of the model).
%! @item DynareOutput
%! Matlab/Octave structure (Results reported by Dynare).
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item DynareOutput
%! Matlab/Octave structure (Results reported by Dynare).
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 2
%! @strong{This function calls:}
%! @ref{dynTime}
%!
%! @end deftypefn
%@eod:
% Copyright (C) 2012 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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% Original author: stephane DOT adjemian AT univ DASH lemans DOT fr
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if DynareModel . maximum_lead
error ( [ ' simul_backward_nonlinear_model:: The specified model is not backward looking!' ] )
end
% Set the covariance matrix of the structural innovations.
variances = diag ( DynareModel . Sigma_e ) ;
number_of_shocks = length ( DynareModel . Sigma_e ) ;
positive_var_indx = find ( variances > 0 ) ;
effective_number_of_shocks = length ( positive_var_indx ) ;
covariance_matrix = DynareModel . Sigma_e ( positive_var_indx , positive_var_indx ) ;
covariance_matrix_upper_cholesky = chol ( covariance_matrix ) ;
% Set seed to its default state.
if DynareOptions . bnlms . set_dynare_seed_to_default
set_dynare_seed ( ' default' ) ;
end
% Simulate structural innovations.
switch DynareOptions . bnlms . innovation_distribution
case ' gaussian'
DynareOutput . bnlms . shocks = randn ( sample_size , effective_number_of_shocks ) * covariance_matrix_upper_cholesky ;
otherwise
error ( [ ' simul_backward_nonlinear_model:: ' DynareOption . bnlms . innovation_distribution ' distribution for the structural innovations is not (yet) implemented!' ] )
end
% Put the simulated innovations in DynareOutput.exo_simul.
DynareOutput . exo_simul = zeros ( sample_size , number_of_shocks ) ;
DynareOutput . exo_simul ( : , positive_var_indx ) = DynareOutput . bnlms . shocks ;
DynareOutput . exo_simul = [ zeros ( 1 , number_of_shocks ) ; DynareOutput . exo_simul ] ;
% Get usefull vector of indices.
ny0 = nnz ( DynareModel . lead_lag_incidence ( 2 , : ) ) ;
ny1 = nnz ( DynareModel . lead_lag_incidence ( 1 , : ) ) ;
iy1 = find ( DynareModel . lead_lag_incidence ( 1 , : ) > 0 ) ;
idx = 1 : DynareModel . endo_nbr ;
jdx = idx + ny1 ;
hdx = 1 : ny1 ;
% Get the name of the dynamic model routine.
model_dynamic = str2func ( [ DynareModel . fname , ' _dynamic' ] ) ;
% initialization of vector y.
y = NaN ( length ( idx ) + ny1 , 1 ) ;
% initialization of the returned simulations.
DynareOutput . endo_simul = NaN ( DynareModel . endo_nbr , sample_size + 1 ) ;
DynareOutput . endo_simul ( : , 1 ) = DynareOutput . steady_state ;
% Simulations (call a Newton-like algorithm for each period).
for it = 2 : sample_size + 1
y ( jdx ) = DynareOutput . endo_simul ( : , it - 1 ) ; % A good guess for the initial conditions is the previous values for the endogenous variables.
y ( hdx ) = y ( jdx ( iy1 ) ) ; % Set lagged variables.
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y ( jdx ) = solve1 ( model_dynamic , y , idx , jdx , 1 , 1 , DynareOptions . gstep , ...
DynareOptions . solve_tolf , DynareOptions . solve_tolx , ...
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DynareOptions . simul . maxit , DynareOptions . debug , ...
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DynareOutput . exo_simul , DynareModel . params , ...
DynareOutput . steady_state , it ) ;
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DynareOutput . endo_simul ( : , it ) = y ( jdx ) ;
end