clear all
close all

x = load('hist_data_no.txt');

time = x(:,1);
gnp = x(:,2);
c = x(:,3);
g = x(:,4);
inv = x(:,5);
ex = x(:,6);
im = x(:,7);
n = length(time);

lgnp = log(gnp);

figure
plot(time,lgnp)
title('gross national product')
ylabel('log')

%% growth rates
gnp_gr_avg = (lgnp(n) - lgnp(1))/(n-7);

% gnp_gr = gnp(2:n)./gnp(1:n-1)-1;
% gnp_gr_avg2 = geomean(1+gnp_gr)-1;

disp('annual average gnp growth rate (1865 - 2008)')
disp([gnp_gr_avg ])  %%gnp_gr_avg2])


%% shares
cy_share = c./gnp;
iy_share = inv./gnp;
gy_share = g./gnp;
nx = ex - im;
nxy_share = nx./gnp;

figure
plot(time,[cy_share, iy_share, gy_share, nxy_share])
legend('C/Y','I/Y','G/Y','NX/Y')
title('shares to gnp')

sample = find(~isnan(gnp));

disp('cy_share, iy_share, gy_share, nxy_share')
disp([mean(cy_share(sample)), mean(iy_share(sample)), mean(gy_share(sample)), mean(nxy_share(sample))])


%% cyclical properties  prewar

w = find(time==1939);
prewar = (1:w)';
t = time(prewar);

lgnp = log(gnp(prewar));
lc = log(c(prewar));
linv = log(inv(prewar));
lg = log(g(prewar));
nxy_share = nx./gnp;
nxy_share = nxy_share(prewar);


[lgnp_trend,lgnp_gap] = hp(lgnp,100);
[lc_trend,lc_gap] = hp(lc,100);
[linv_trend,linv_gap] = hp(linv,100);
[lg_trend,lg_gap] = hp(lg,100);
[nxy_share_trend,nxy_share_gap] = hp(nxy_share,100);

figure
plot(t,[lgnp_gap, lc_gap])
legend('gap gnp','gap c')

figure
plot(t,[lgnp_gap, linv_gap])
legend('gap gnp','gap inv')

figure
plot(t,[lgnp_gap, lg_gap])
legend('gap gnp','gap g')

figure
plot(t,[lgnp_gap, nxy_share_gap])
legend('gap gnp','gap nx share')

save prewar.mat

%% cyclical properties  postwar

ww = find(time==1946);
postwar = (ww:n)';
t = time(postwar);

lgnp = log(gnp(postwar));
lc = log(c(postwar));
linv = log(inv(postwar));
lg = log(g(postwar));
nxy_share = nx./gnp;
nxy_share = nxy_share(postwar);

[lgnp_trend,lgnp_gap] = hp(lgnp,100);
[lc_trend,lc_gap] = hp(lc,100);
[linv_trend,linv_gap] = hp(linv,100);
[lg_trend,lg_gap] = hp(lg,100);
[nxy_share_trend,nxy_share_gap] = hp(nxy_share,100);

figure
plot(t,[lgnp_gap, lc_gap])
legend('gap gnp','gap c')

figure
plot(t,[lgnp_gap, linv_gap])
legend('gap gnp','gap inv')

figure
plot(t,[lgnp_gap, lg_gap])
legend('gap gnp','gap g')

figure
plot(t,[lgnp_gap, nxy_share_gap])
legend('gap gnp','gap nx share')

save postwar.mat

cc = corrcoef(lgnp_gap,lc_gap);
cg = corrcoef(lgnp_gap,lg_gap);
ci = corrcoef(lgnp_gap,linv_gap);
cnx = corrcoef(lgnp_gap,nxy_share_gap);

disp('contemporaneous correlation coefficient with GNP')
disp('            C            INV              G            NX share')
disp([cc(1,2) cg(1,2) ci(1,2) cnx(1,2)])