function [s,desvabs] = hpfilter(y,w,plotter)
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% Author: Wilmer Henao wi-henao@uniandes.edu.co
% Department of Mathematics
% Universidad de los Andes
% Colombia
%
% Hodrick-Prescott filter extracts the trend of a time series, the output
% is not a formula but a new filtered time series. This trend can be
% adjusted with parameter w; values for w lie usually in the interval
% [100,20000], and it is up to you to use the one you like, As w approaches infty,
% H-P will approach a line. If the series doesn't have a trend p.e.White Noise,
% doing H-P is meaningles
%
% [s] = hpfilter(y,w)
% w = Smoothing parameter (Economists advice: "Use w = 1600 for quarterly data")
% y = Original series
% s = Filtered series
% This program can work with several series at a time, as long as the
% number of series you are working with doesn't exceed the number of
% elements in the series + it uses sparse matrices which improves speed
% and performance in the longest series
%
% [s] = hpfilter(y,w,'makeplot')
% 'makeplot' in the input, plots the graphics of the original series
% against the filtered series, if more than one series is being
% considered the program will plot all of them in different axes
%
% [s,desvabs] = hpfilter(y,w)
% Gives you a mesure of the standardized differences in absolute values
% between the original and the filtered series. A big desvabs means
% that the series implies a large relative volatility.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tic
if nargin < 2
error('Requires at least two arguments.');
end
[m,n] = size (y);
if m < n
y = y'; m = n;
end
d = repmat([w -4*w ((6*w+1)/2)], m, 1);
d(1,2) = -2*w; d(m-1,2) = -2*w;
d(1,3) = (1+w)/2; d(m,3) = (1+w)/2;
d(2,3) = (5*w+1)/2; d(m-1,3) = (5*w+1)/2;
B = spdiags(d, -2:0, m, m); %I use a sparse version of B, because when m is large, B will have many zeros
B = B+B';
s = B\y;
if nargin == 3
t = size(y,2);
for i = 1:t
figure(i)
plot(s(:,i),'r'); grid on; hold on; plot(y(:,i)); title(['Series #',num2str(i)]);
end
end
if nargout == 2
desvabs = mean(abs(y-s)./s);
end
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