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function DynareOutput = simul_backward_nonlinear_model ( initial_conditions, sample_size, DynareOptions, DynareModel, DynareOutput, innovations)
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% Simulates a stochastic non linear backward looking model with arbitrary precision (a deterministic solver is used).
%
% INPUTS
% - initial_conditions [double] n*1 vector, initial conditions for the endogenous variables.
% - sample_size [integer] scalar, number of periods for the simulation.
% - DynareOptions [struct] Dynare's options_ global structure.
% - DynareModel [struct] Dynare's M_ global structure.
% - DynareOutput [struct] Dynare's oo_ global structure.
% - innovations [double] T*q matrix, innovations to be used for the simulation.
%
% OUTPUTS
% - DynareOutput [struct] Dynare's oo_ global structure.
%
% REMARKS
% [1] The innovations used for the simulation are saved in DynareOutput.exo_simul, and the resulting paths for the endogenous
% variables are saved in DynareOutput.endo_simul.
% [2] The last input argument is not mandatory. If absent we use random draws and rescale them with the informations provided
% through the shocks block.
% [3] If the first input argument is empty, the endogenous variables are initialized with 0, or if available with the informations
% provided thrtough the histval block.
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% Copyright (C) 2012-2017 Dynare Team
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%
% 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/>.
if DynareModel . maximum_lead
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error ( ' simul_backward_nonlinear_model:: The specified model is not backward looking!' )
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end
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if nargin < 6
% 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 ] ;
else
DynareOutput . exo_simul = innovations ;
end
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% Get usefull vector of indices.
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' ] ) ;
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model_dynamic_s = str2func ( ' dynamic_backward_model_for_simulation' ) ;
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% 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 ) ;
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if isempty ( initial_conditions )
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if isfield ( DynareModel , ' endo_histval' )
DynareOutput . endo_simul ( : , 1 : DynareModel . maximum_lag ) = DynareModel . endo_histval ;
else
warning ( ' simul_backward_nonlinear_model:: Initial condition is zero for all variables! If the model is nonlinear, the model simulation may fail with the default initialization' )
DynareOutput . endo_simul ( : , 1 ) = 0 ;
end
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else
DynareOutput . endo_simul ( : , 1 ) = initial_conditions ;
end
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Y = DynareOutput . endo_simul ;
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% Simulations (call a Newton-like algorithm for each period).
for it = 2 : sample_size + 1
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ylag = Y ( iy1 , it - 1 ) ; % Set lagged variables.
y = Y ( : , it - 1 ) ; % A good guess for the initial conditions is the previous values for the endogenous variables.
Y ( : , it ) = dynare_solve ( model_dynamic_s , y , DynareOptions , model_dynamic , ylag , DynareOutput . exo_simul , DynareModel . params , DynareOutput . steady_state , it ) ;
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end
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DynareOutput . endo_simul = Y ;