clear all
close all

x = load('us.txt');
time = x(:,1);
gdp = x(:,2);
c = x(:,3);
cpi = x(:,4);
ir = x(:,5);
w = x(:,6);
inv = x(:,7);

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

lcpi = log(cpi);
ir = ir/100;
lw = log(w);
linv = log(inv);

[lgdp_trend,lgdp_gap] = hp(lgdp,1600);
[lc_trend,lc_gap] = hp(lc,1600);
[linv_trend,linv_gap] = hp(linv,1600);

figure
plot(time,[lgdp_gap, lc_gap])
legend('gap gdp','gap c')

figure
plot(time,[lgdp_gap, linv_gap])
legend('gap gdp','gap inv')

c1 = corrfn(lgdp_gap,lc_gap,5);
c2 = corrfn(lgdp_gap,linv_gap,5);

k = (5:-1:-5)';

[k c1]
[k c2]

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

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

cy_ratio = c ./ gdp;
iy_ratio = inv./ gdp;
avg_cy = mean(cy_ratio);
avg_iy = mean(iy_ratio);

std_y = std(lgdp_gap);
std_c = std(lc_gap);
std_inv = std(linv_gap);

disp('Share to GDP:  C          I')
disp([avg_cy   avg_iy])
disp('Standard deviation: Y     C      I')
disp([std_y   std_c  std_inv]*100)


% inflation
pie4 = lcpi(5:end) - lcpi(1:end-4);
pie4 = [nan(4,1);pie4];

%rir
rir = ir(1:end-4) - pie4(5:end);
rir = [rir;ones(4,1)*nan];

[pie4_trend,pie4_gap] = hp(pie4,1600);
[rir_trend, rir_gap] = hp(rir,1600);

c3 = corrfn(lgdp_gap,pie4_gap,5);
c4 = corrfn(lgdp_gap,rir_gap,5);

figure
plot(time,[lgdp_gap, pie4_gap])
legend('gap gdp','gap \pi')

figure
plot(time,[lgdp_gap, rir_gap])
legend('gap gdp', 'gap rir')

figure
bar(k,c3)
xlabel('k')
ylabel('corr. coef.')
title('HDP_t x \pi_{t+k}')

figure
bar(k,c4)
xlabel('k')
ylabel('corr. coef.')
title('HDP_t x RIR_{t+k}')

%% test vyznamnosti koeficientu korelace
n = length(time);

test.c = [c1 k corrtest(c1,n)];
test.i = [c2 k corrtest(c2,n)];
test.pie = [c3 k corrtest(c3,n-4)];
test.rir = [c4 k corrtest(c4,n-4)];