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function [hptrend,hpcycle] = sample_hp_filter(y,s)
% HP filters a collection of time series.
%
% INPUTS
% y [double] T*n matrix of data (n is the number of variables)
% s [double] scalar, smoothing parameter.
%
% OUTPUTS
% hptrend [double] T*n matrix, trend component of y.
% hpcycle [double] T*n matrix, cycle component of y.
%
% SPECIAL REQUIREMENTS
%
% Copyright (C) 2010-2011 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/>.
[T,n] = size(y);
if nargin<2
s = 1600;
end
D = spdiags(repmat([s, -4.0*s, (1 + 6.0*s), -4.0*s, s], T, 1), -2:2, T, T);% Sparse matrix.
D(1,1) = 1.0+s; D(T,T) = D(1,1);
D(1,2) = -2.0*s; D(2,1) = D(1,2); D(T-1,T) = D(1,2); D(T,T-1) = D(1,2);
D(2,2) = 1.0+5.0*s; D(T-1,T-1) = D(2,2);
hptrend = D\y;
hpcycle = y-hptrend;
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