function simulation = simul_backward_model(initialconditions, samplesize, innovations)
% Simulates a stochastic backward looking model (with arbitrary precision).
%
% INPUTS
% - initialconditions [double] n*1 vector, initial conditions for the endogenous variables.
% - samplesize [integer] scalar, number of periods for the simulation.
% - innovations [dseries] innovations to be used for the simulation.
%
% OUTPUTS
% - simulation [dseries] Simulated endogenous and exogenous variables.
%
% 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.
% Copyright (C) 2012-2017 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 .
global options_ M_ oo_
if nargin<3
Innovations =[];
else
if isdseries(innovations)
if isequal(innovations.dates(1)-1, initialconditions.dates(end))
if innovations.nobs