%% HP filter for theta 
%% Pmk times series 
% 1980Q1-2020Q2, import price of intermediate goods

function xx=AR1hp_c_e_pmk(xx)

data = xlsread('NewKoreanData.xlsx','Shocks','B85:B246'); 

data = log(data);

[~, data] = hpfilter(data,1600);

xx = AR1e(data);
function rmse = AR1e(y)
x = y(1:end-1);
y = y(2:end);
n = length(x);
x = [ones(n,1) x];
B = (x'*x)\(x'*y);

e = y - x*B;
s2 = e'*e/(n-2);

rmse = sqrt(s2);
end

end