clear all
close all
set(0,'defaultlinelinewidth',1.5);

% load data
d = dbload('us_quarterly.csv');

%% get ranges
first_date = get(d.gdp,'first');
last_date  = get(d.gdp,'last');
rng_all    = get(d.gdp,'range');
rng        = qq(1970,1):enddate(d.gdp);  % selected range

%%hezci zobrazeni range
% dat2str(rng)'

%%vyber casove rady
% d.gdp(rng)   % cisla
% d.gdp{rng}   % casova rada

%% logaritmus
% Why?  difference is percentage change

d.l_gdp = 100*log(d.gdp);

% plot graphs
figure
plot(d.gdp)
title('GDP, level, billions of dollars')
grid

figure
plot(d.l_gdp)
title('GDP, 100*log')
grid

% Task: plot selected range


return
%% Linerani trend 

d.l_gdp_ltrend = trend(d.l_gdp,'connect=',false);  % iris function
d.l_gdp_lgap   = d.l_gdp - d.l_gdp_ltrend;


figure
plot([d.l_gdp d.l_gdp_ltrend])
legend('log HDP','linearni trend','Location','NorthWest')
title('Linearni trend')
grid

figure
plot(d.l_gdp_lgap)
title('Odchylka od linearniho trendu')
ylabel('%')
grid

%% tempa rustu

% mezictvrtletni, annualizovane
d.dla_gdp  = diff(d.l_gdp)*4;
% alternativni zpusob zapisu
d.dla_gdp2 = (d.l_gdp - d.l_gdp{-1})*4;   % alternative way

figure
plot(d.dla_gdp)
title('Mezictvrtlentí tempo rustu, (q-on-q), % annualizovane')
grid

% mezirocni 




% Task: porovnejte s vypoctem z nelogaritmovane rady, fce: pct


%% Hodrick-Prescott filtr

[d.l_gdp_trend, d.l_gdp_gap] = hpf(d.l_gdp,'lambda=',1600);

figure
plot([d.l_gdp d.l_gdp_trend])
title('Real GDP, 100*log')
legend('level','trend','Location','NorthWest')
grid

figure
plot([d.l_gdp_gap])
title('Real GDP gap, %')
ylabel('% deviation from trend')
grid

% Task: Try different lambda




%% Band-pass filter

% frequencies of business cycle  (lower is trend, higher are statistical
% discrepancies)

low  = 8;
high = 32;

[d.l_gdp_bpgap] = bpass(d.l_gdp,[low high]);

figure
plot([d.l_gdp_bpgap d.l_gdp_gap])
title('Real GDP gap, %')
ylabel('% deviation from trend')
legend('Band pass filter','HP filter')
grid

% set(gcf,'Papersize',[32 26]);
% set(gcf,'PaperPosition',[0 0 32 26]);
% saveas(gcf,'filters_comparison','pdf');

%%  statisticke charakteristiky

% tempo rustu
gr.mean = mean(d.d4l_gdp);
gr.std  = std(d.d4l_gdp);
gr.min  = min(d.d4l_gdp);
gr.max  = max(d.d4l_gdp);
gr.ac   = acfn(d.d4l_gdp,5);

gr.pct_pos  = length(find(d.d4l_gdp >0))/length(d.d4l_gdp);   
gr.pct_high = length(find(d.d4l_gdp > gr.mean))/length(d.d4l_gdp);

% HP filtr

disp('Tempo rustu')
gr