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function forecasts = backward_model_forecast(initialcondition, listofvariables, periods, withuncertainty)
% Returns unconditional forecasts.
%
% INPUTS
% - initialcondition [dseries] Initial conditions for the endogenous variables.
% - periods [integer] scalar, the number of (forecast) periods.
% - withuncertainty [logical] scalar, returns confidence bands if true.
%
% OUTPUTS
% - forecast [dseries]
% Copyright (C) 2017-2018 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 <https://www.gnu.org/licenses/>.
global M_ options_ oo_
% Check that the model is actually backward
if M_.maximum_lead
error(['backward_model_forecast:: The specified model is not backward looking!'])
end
% Initialize returned argument.
forecasts = struct();
% Set defaults.
if nargin<2
listofvariables = M_.endo_names;
periods = 8;
withuncertainty = false;
end
if nargin<3
periods = 8;
withuncertainty = false;
end
if nargin<4
withuncertainty = false;
end
start = initialcondition.dates(end)+1;
% Set default initial conditions for the innovations.
for i=1:M_.exo_nbr
if ~ismember(M_.exo_names{i}, initialcondition.name)
initialcondition{M_.exo_names{i}} = dseries(zeros(initialcondition.nobs, 1), initialcondition.dates(1), M_.exo_names{i});
end
end
% Set up initial conditions
[initialcondition, periods, innovations, DynareOptions, DynareModel, DynareOutput, endonames, exonames, nx, ny1, iy1, jdx, model_dynamic, y] = ...
simul_backward_model_init(initialcondition, periods, options_, M_, oo_, zeros(periods, M_.exo_nbr));
% Get vector of indices for the selected endogenous variables.
n = length(listofvariables);
idy = zeros(n,1);
for i=1:n
j = find(strcmp(listofvariables{i}, endonames));
if isempty(j)
error('backward_model_forecast:: Variable %s is unknown!', listofvariables{i})
else
idy(i) = j;
end
end
% Set the number of simulations (if required).
if withuncertainty
B = 1000;
end
% Get the covariance matrix of the shocks.
if withuncertainty
Sigma = M_.Sigma_e + 1e-14*eye(M_.exo_nbr);
sigma = transpose(chol(Sigma));
end
% Compute forecast without shock
if options_.linear
ysim__0 = simul_backward_linear_model_(initialcondition, periods, DynareOptions, DynareModel, DynareOutput, innovations, nx, ny1, iy1, jdx, model_dynamic);
else
ysim__0 = simul_backward_nonlinear_model_(initialcondition, periods, DynareOptions, DynareModel, DynareOutput, innovations, iy1, model_dynamic);
end
forecasts.pointforecast = dseries(transpose(ysim__0(idy,:)), initialcondition.init, listofvariables);
% Set first period of forecast
forecasts.start = start;
if withuncertainty
% Preallocate an array gathering the simulations.
ArrayOfForecasts = zeros(n, periods+initialcondition.nobs, B);
for i=1:B
innovations = transpose(sigma*randn(M_.exo_nbr, periods));
if options_.linear
[ysim__, xsim__] = simul_backward_linear_model_(initialcondition, periods, DynareOptions, DynareModel, DynareOutput, innovations, nx, ny1, iy1, jdx, model_dynamic);
else
[ysim__, xsim__] = simul_backward_nonlinear_model_(initialcondition, periods, DynareOptions, DynareModel, DynareOutput, innovations, iy1, model_dynamic);
end
ArrayOfForecasts(:,:,i) = ysim__(idy,:);
end
% Compute mean (over future uncertainty) forecast.
forecasts.meanforecast = dseries(transpose(mean(ArrayOfForecasts, 3)), initialcondition.init, listofvariables);
forecasts.medianforecast = dseries(transpose(median(ArrayOfForecasts, 3)), initialcondition.init, listofvariables);
forecasts.stdforecast = dseries(transpose(std(ArrayOfForecasts, 1,3)), initialcondition.init, listofvariables);
% Compute lower and upper 95% confidence bands
ArrayOfForecasts = sort(ArrayOfForecasts, 3);
forecasts.lb = dseries(transpose(ArrayOfForecasts(:,:,round(0.025*B))), initialcondition.init, listofvariables);
forecasts.ub = dseries(transpose(ArrayOfForecasts(:,:,round(0.975*B))), initialcondition.init, listofvariables);
end
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