sample_hp_filter

 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

0001 function [hptrend,hpcycle] = sample_hp_filter(y,s)
0002 % HP filters a collection of time series.
0003 %
0004 % INPUTS
0005 %   y                        [double]   T*n matrix of data (n is the number of variables)
0006 %   s                        [double]   scalar, smoothing parameter.
0007 %
0008 % OUTPUTS
0009 %   hptrend                  [double]   T*n matrix, trend component of y.
0010 %   hpcycle                  [double]   T*n matrix, cycle component of y.
0011 %
0012 % SPECIAL REQUIREMENTS
0013 %
0014 
0015 % Copyright (C) 2010-2011 Dynare Team
0016 %
0017 % This file is part of Dynare.
0018 %
0019 % Dynare is free software: you can redistribute it and/or modify
0020 % it under the terms of the GNU General Public License as published by
0021 % the Free Software Foundation, either version 3 of the License, or
0022 % (at your option) any later version.
0023 %
0024 % Dynare is distributed in the hope that it will be useful,
0025 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0026 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0027 % GNU General Public License for more details.
0028 %
0029 % You should have received a copy of the GNU General Public License
0030 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
0031 
0032 [T,n] = size(y);
0033 
0034 if nargin<2
0035     s = 1600;
0036 end
0037 
0038 D = spdiags(repmat([s, -4.0*s, (1 + 6.0*s), -4.0*s, s], T, 1), -2:2, T, T);% Sparse matrix.
0039 D(1,1) = 1.0+s; D(T,T) = D(1,1);
0040 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);
0041 D(2,2) = 1.0+5.0*s; D(T-1,T-1) = D(2,2);
0042 
0043 hptrend = D\y;
0044 hpcycle = y-hptrend;