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function yhat = fn_forecast(Bh,phi,nn,nexo,Xfexo)
% yhat = fn_forecast(Bh,phi,nn,nexo,Xfexo)
% Unconditional forecating without shocks.
% y_hat(t+h) = c + x_hat(t+h-1)*Bh, X: 1*k; Bh: k*nvar; y_hat: 1*nvar
%
% Bh: k-by-nvar, the (posterior) estimate of B.
% phi: the 1-by-(nvar*lags+nexo) data matrix X where k=nvar*lags+1
% (last period plus lags before the beginning of forecast).
% nn: [nvar,lags,nfqm], nfqm: forecast periods (months or quarters).
% nexo: number of exogenous variables. The constant term is the default setting.
% Besides this term, we have nexo-1 exogenous variables.
% Xfexo: nfqm-by-nexo-1 vector of exoenous variables in the forecast horizon where
% nfqm: number of forecast periods.
%-----------
% yhat: nfqm-by-nvar forecast.
%
% See fn_forecastsim.m with shocks; fn_forecaststre.m.
%
% Copyright (C) 1997-2012 Tao Zha
%
% This 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.
%
% It 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.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
if nargin == 3
nexo=1; % default for constant term
elseif nexo<1
error('We need at least one exogenous term so nexo must >= 1')
end
% ** setup
nvar = nn(1);
lags = nn(2);
nfqm = nn(3);
tcwx = nvar*lags; % total coefficeint without exogenous variables
if nexo>1
if (nfqm > size(Xfexo,1))
disp(' ')
warning('Make sure the forecast horizon in the exogenous variable matrix Xfexo > forecast periods')
disp('Press ctrl-c to abort')
pause
elseif ((nexo-1) ~= size(Xfexo,2))
disp(' ')
warning('Make sure that nexo matchs the exogenous variable matrix Xfexo')
disp('Press ctrl-c to abort')
pause
end
end
% ** reconstruct x(t) for y(t+h) = x(t+h-1)*B
% ** where phi = x(t+h-1) with last column being constant
yhat = zeros(nfqm,nvar);
for k=1:nfqm
yhat(k,:) = phi*Bh;
%*** lagged endogenous variables
phi(1,nvar+1:tcwx) = phi(1,1:tcwx-nvar);
phi(1,1:nvar) = yhat(k,:);
%*** exogenous variables excluding constant terms
if (nexo>1)
phi(1,tcwx+1:tcwx+nexo-1) = Xfexo(k,:);
end
end
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