clear all
close all

x = load('us.txt');
t = x(:,1);
gdp = x(:,2);
c = x(:,3);
cpi = x(:,4);
ir = x(:,5);
w = x(:,6);
inv = x(:,7);
n = length(t);

lgdp = log(gdp);
lc = log(c);

lcpi = log(cpi);
lw = log(w);
linv = log(inv);

[lgdp_trend,lgdp_gap] = hp(lgdp,1600);
std_y = std(lgdp_gap);

%% spotreba
[lc_trend,lc_gap] = hp(lc,1600);

figure
plot(t,[lgdp_gap, lc_gap])
legend('gap gdp','gap c')

c1 = corrfn(lgdp_gap,lc_gap,5);

k = (5:-1:-5)';
[k c1]

figure
bar(k,c1)
xlabel('k')
ylabel('corr. coef.')
title('HDP_t vs. C_{t+k}')

test.c = [c1 k corrtest(c1,n)];
std_c = std(lc_gap);









return
%% investice

[linv_trend,linv_gap] = hp(linv,1600);

figure
plot(t,[lgdp_gap, linv_gap])
legend('gap gdp','gap i')

c2 = corrfn(lgdp_gap,linv_gap,5);

figure
bar(k,c2)
xlabel('k')
ylabel('corr. coef.')
title('HDP_t vs. I_{t+k}')

test.inv = [c2 k corrtest(c2,n)];
std_inv = std(linv_gap);