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function [y_,int_width,int_width_ME]=simultxdet(y0,ex,ex_det, iorder,var_list,M_,oo_,options_)
%function [y_,int_width,int_width_ME]=simultxdet(y0,ex,ex_det, iorder,var_list,M_,oo_,options_)
%
% Simulates a stochastic model in the presence of deterministic exogenous shocks
%
% INPUTS:
% y0: initial values, of length M_.maximum_lag
% ex: matrix of stochastic exogenous shocks, starting at period 1
% ex_det: matrix of deterministic exogenous shocks, starting at period 1-M_.maximum_lag
% iorder: order of approximation
% var_list: list of endogenous variables to simulate
% M_: Dynare model structure
% oo_: Dynare results structure
% options_: Dynare options 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
% int_width_ME:distance between upper bound and
% mean forecast when considering measurement error
%
% The forecast horizon is equal to size(ex, 1).
% The condition size(ex,1)+M_.maximum_lag=size(ex_det,1) must be verified
% for consistency.
% Copyright © 2008-2018 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/>.
if options_.order>2
error('simultxdet.m: Forecasting with varexo_det does not support order>2.')
elseif options_.order==2 && options_.pruning
error('simultxdet.m: Forecasting with varexo_det does not support pruning.')
end
dr = oo_.dr;
ykmin = M_.maximum_lag;
endo_nbr = M_.endo_nbr;
exo_det_steady_state = oo_.exo_det_steady_state;
nstatic = M_.nstatic;
nspred = M_.nspred;
nc = size(dr.ghx,2);
iter = size(ex,1);
if size(ex_det, 1) ~= iter+ykmin
error('Size mismatch: number of forecasting periods for stochastic exogenous and deterministic exogenous don''t match')
end
y_ = zeros(size(y0,1),iter+ykmin);
y_(:,1:ykmin) = y0;
k1 = ykmin:-1:1;
k2 = dr.kstate(find(dr.kstate(:,2) <= ykmin+1),[1 2]);
k2 = k2(:,1)+(ykmin+1-k2(:,2))*endo_nbr;
k3 = M_.lead_lag_incidence(1:ykmin,:)';
k3 = find(k3(:));
k4 = dr.kstate(find(dr.kstate(:,2) < ykmin+1),[1 2]);
k4 = k4(:,1)+(ykmin+1-k4(:,2))*endo_nbr;
nvar = length(var_list);
if nvar == 0
nvar = endo_nbr;
ivar = 1:nvar;
else
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
end
if iorder == 1
for i = ykmin+1: iter+ykmin
tempx1 = y_(dr.order_var,k1);
tempx2 = tempx1-repmat(dr.ys(dr.order_var),1,ykmin);
tempx = tempx2(k2);
y_(dr.order_var,i) = dr.ys(dr.order_var)+dr.ghx*tempx+dr.ghu*ex(i-ykmin,:)';
for j=1:min(ykmin+M_.exo_det_length+1-i,M_.exo_det_length)
y_(dr.order_var,i) = y_(dr.order_var,i) + dr.ghud{j}*(ex_det(i+j-1,:)'-exo_det_steady_state);
end
k1 = k1+1;
end
elseif iorder == 2
for i = ykmin+1: iter+ykmin
tempx1 = y_(dr.order_var,k1);
tempx2 = tempx1-repmat(dr.ys(dr.order_var),1,ykmin);
tempx = tempx2(k2);
tempu = ex(i-ykmin,:)';
tempuu = kron(tempu,tempu);
tempxx = kron(tempx,tempx);
tempxu = kron(tempx,tempu);
y_(dr.order_var,i) = dr.ys(dr.order_var)+dr.ghs2/2+dr.ghx*tempx+ ...
dr.ghu*tempu+0.5*(dr.ghxx*tempxx+dr.ghuu*tempuu)+dr.ghxu* ...
tempxu;
for j=1:min(ykmin+M_.exo_det_length+1-i,M_.exo_det_length)
tempud = ex_det(i+j-1,:)'-exo_det_steady_state;
tempudud = kron(tempud,tempud);
tempxud = kron(tempx,tempud);
tempuud = kron(tempu,tempud);
y_(dr.order_var,i) = y_(dr.order_var,i) + dr.ghud{j}*tempud + ...
dr.ghxud{j}*tempxud + dr.ghuud{j}*tempuud + ...
0.5*dr.ghudud{j,j}*tempudud;
for k=1:j-1
tempudk = ex_det(i+k-1,:)'-exo_det_steady_state;
tempududk = kron(tempudk,tempud);
y_(dr.order_var,i) = y_(dr.order_var,i) + ...
dr.ghudud{k,j}*tempududk;
end
end
k1 = k1+1;
end
else
error('simultxdet.m: order>2 not supported.')
end
[A,B] = kalman_transition_matrix(dr,nstatic+(1:nspred),1:nc);
inv_order_var = dr.inv_order_var;
ghx1 = dr.ghx(inv_order_var(ivar),:);
ghu1 = dr.ghu(inv_order_var(ivar),:);
sigma_u = B*M_.Sigma_e*B';
sigma_u1 = ghu1*M_.Sigma_e*ghu1';
sigma_y = 0;
var_yf=NaN(iter,nvar); %initialize
for i=1:iter
sigma_y1 = ghx1*sigma_y*ghx1'+sigma_u1; %only valid at first order, needs to be fixed, see https://git.dynare.org/Dynare/dynare/-/issues/1940
var_yf(i,:) = diag(sigma_y1)';
if i == iter
break
end
sigma_u = A*sigma_u*A';
sigma_y = sigma_y+sigma_u;
end
fact = norminv((1-options_.forecasts.conf_sig)/2,0,1);
if nargout==3
var_yf_ME=var_yf;
var_yf_ME(:,options_.varobs_id)=var_yf(:,options_.varobs_id)+repmat(diag(M_.H)',horizon,1);
int_width_ME = zeros(horizon,M_.endo_nbr);
end
int_width = zeros(iter,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
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