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function rootsinv = fn_varoots(Bhat,nvar,lags)
%
% Using eigenvalues to find the inverse of all roots associated with the VAR proceess:
% y_t' = C + y_{t-1}'*B_1 + ... + Y_{t-p}'*B_p + u_t'.
% where columns correspond to equations. See also Judge (1), pp.753-755 where rows correspond to equations.
% Bhat: ncoef-by-nvar where ncoef=nvar*lags+nexo and nvar is the number of endogenous variables.
% Columns corresponds to equations with
% ncoef=[nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
% ..., nvar coef in the last lag, and nexo coefficients.
% Note that entries in the rows of Bhat that > nvar*lags are irrelevant.
% nvar: number of endogenous variables.
% lags: number of lags.
%-------
% rootsinv: a vector of nvar*lags inverse roots. When > 1, explosive. When all < 1, stationary.
%
% Tao Zha, September 2000
%
% 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 size(Bhat,1)<nvar*lags
disp(' ')
warning('Make sure that Bhat has at least nvar*lags rows')
return
end
%--------- Strack the VAR(p) to the VAR(1) with z_t = Az_{t-1}.
%
A1 = diag(ones(nvar*(lags-1),1));
A2 = [A1 zeros(nvar*(lags-1),nvar)];
A = [Bhat(1:nvar*lags,:)'; A2];
rootsinv=eig(A);
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