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function [yf,int_width,int_width_ME]=forcst(dr,y0,horizon,var_list,M_,oo_,options_)
% function [yf,int_width,int_width_ME]=forecst(dr,y0,horizon,var_list,M_,oo_,options_)
% computes mean forecast for a given value of the parameters
% computes also confidence band for the forecast
%
% INPUTS:
% dr: structure containing decision rules
% y0: initial values
% horizon: nbr of periods to forecast
% var_list: list of variables (character matrix)
% M_: Dynare model structure
% options_: Dynare options structure
% oo_: Dynare results structure
% OUTPUTS:
% yf: mean forecast
% int_width: distance between upper bound and
% mean forecast
% int_width_ME:distance between upper bound and
% mean forecast when considering measurement error
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2003-2019 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/>.
oo_=make_ex_(M_,options_,oo_);
yf = simult_(M_,options_,y0,dr,zeros(horizon,M_.exo_nbr),1);
nstatic = M_.nstatic;
nspred = M_.nspred;
nc = size(dr.ghx,2);
endo_nbr = M_.endo_nbr;
inv_order_var = dr.inv_order_var;
[A,B] = kalman_transition_matrix(dr,nstatic+(1:nspred),1:nc,M_.exo_nbr);
if isempty(var_list)
var_list = M_.endo_names(1:M_.orig_endo_nbr);
end
nvar = length(var_list);
ivar = zeros(nvar, 1);
for i=1:nvar
i_tmp = strmatch(var_list{i}, M_.endo_names, 'exact');
if isempty(i_tmp)
disp(var_list{i});
error ('One of the variable specified does not exist') ;
else
ivar(i) = i_tmp;
end
end
ghx1 = dr.ghx(inv_order_var(ivar),:);
ghu1 = dr.ghu(inv_order_var(ivar),:);
%initialize recursion
sigma_u = B*M_.Sigma_e*B';
sigma_u1 = ghu1*M_.Sigma_e*ghu1';
sigma_y = 0; %no uncertainty about the states
var_yf = NaN(horizon,nvar); %initialize
for i = 1:horizon
%map uncertainty about states into uncertainty about observables
sigma_y1 = ghx1*sigma_y*ghx1'+sigma_u1;
var_yf(i,:) = diag(sigma_y1)';
if i == horizon
break
end
%update uncertainty about states
sigma_u = A*sigma_u*A';
sigma_y = sigma_y+sigma_u;
end
if nargout==3
var_yf_ME=var_yf;
[loc_H, loc_varlist] = ismember(options_.varobs', options_.varlist);
loc_varlist(loc_varlist==0) = [];
if ~isempty(loc_varlist)
var_yf_ME(:,loc_varlist) = var_yf(:,loc_varlist)+repmat(diag(M_.H(loc_H,loc_H))', horizon, 1);
end
int_width_ME = zeros(horizon, nvar);
end
fact = norminv((1-options_.forecasts.conf_sig)/2, 0, 1);
int_width = zeros(horizon, nvar);
for i = 1:nvar
int_width(:,i) = -fact*sqrt(var_yf(:,i));
if nargout==3
int_width_ME(:,i) = -fact*sqrt(var_yf_ME(:,i));
end
end
yf = yf(ivar,:);
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