function [tau, F] = myHPfilter(y,mu);

%This function is an HP filter
% Input: 
%        y - a Tx1 data vector
%        mu - the smoothing parameter
%             (use: 1600 for quarterly data, 400 for annual?)
% Output: 
%        tau - sequence of taus which just are the trend

T = size(y,1);

coefs = [1 -4 6 -4 1];
% Frows = zeros(1,T);
 
F = zeros(T,T+4);
for i = 1:1:T
    F(i,i:1:i+4) = coefs;
end
F = F(:,3:T+2);
%Do the endpoints by hand
F(1,1:3) = [1 -2 1];
F(2,1:4) = [-2 5 -4 1];
F((T-1),(T-3):T) = [1 -4 5 -2];
F(T,(T-2):T) = [1 -2 1];

tau = inv(mu*F + eye(T,T))*y;