%
% ch3ex1.m is an example matlab file to read in 
% deJongs rbc data and filter it
%

%format bank

% ----- simulate different types of growths ----- %
% - time trend - %

for j = 1:25
    coef=rand(1);
 for i = 1:150
  tt(i,j) = i*log(1+coef) + randn(1);
 end
 end
 
% - stochastic trend - %

st(1,1:25) = 0;

for j = 1:25
 coef=rand(1);
 for i = 1:149
  st(i+1,j) = coef + st(i,j) + randn(1);
 end
 end
    
    
figure(1)
 subplot(2,1,1); plot(tt)
 subplot(2,1,2); plot(st)
 

% ----- load data from dejong ----- %

X = load('rbc1.txt') ;

% - log real personal total expenditures

c = log(X(:,1));
nsac = log(X(:,6));

% - log Real Personal Consumption Expenditures: Nondurable Goods

cnd = log(X(:,2));

% - log Real Gross Private Domestic Investment
inv = log(X(:,3));

% - Nonfarm Business Sector: Hours of All Persons
h = log(X(:,4));

% ----- make time trend ----- %

time=[1948:.25:2004.75]';

% ----- filter the series for the trend ----- %

tc   = hpfilter(c,1600);
tcnd = hpfilter(cnd,1600);
tinv = hpfilter(inv,1600);
th   = hpfilter(h,1600);

% ----- filter the detrended series ----- %

sc   = c - tc;
scnd = cnd - tcnd;
sinv = inv - tinv;
sh   = h - th ;

% ---- plot graphs of series and hp trend trend ------ %

figure(2)
subplot(2,2,1); plot(time,c,time,tc)
subplot(2,2,2); plot(time,cnd,time,tcnd)
subplot(2,2,3); plot(time,inv,time,tinv)
subplot(2,2,4); plot(time,h,time,th)

% ----- plot stationry hp series ----- %

figure(3)
subplot(2,2,1); plot(time,sc)
subplot(2,2,2); plot(time,scnd)
subplot(2,2,3); plot(time,sinv)
subplot(2,2,4); plot(time,sh)

% ----- bandpass the series ----- % 

[bpc]   = bpass(c,6,40);
[bpcnd] = bpass(cnd,6,40);
[bpinv] = bpass(inv,6,40);
[bph]   = bpass(h,6,40);

[bpnsac]   = bpass(nsac,6,40);

% ----- plot bandpass graphs ---- %

figure(4)
subplot(2,2,1); plot(time,bpc)
subplot(2,2,2); plot(time,bpcnd)
subplot(2,2,3); plot(time,bpinv)
subplot(2,2,4); plot(time,bph)

% --- plot bandpass of sa and nsa ----- %

figure(5)
subplot(2,1,1); plot(time,bpc)
subplot(2,1,2); plot(time,bpnsac)

% ----- compute summary stats ----- %
% - std deviation - %
std([bpc bpcnd bpinv bph ])

% - correlation coeff - %
corrcoef([bpc bpcnd bpinv bph ])

% - auto correlation - %
corrcoef([bpc(3:228) bpc(2:227) bpc(1:226)])
corrcoef([bph(3:228) bpc(2:227) bph(1:226)])


% ----- simulate the economy from midterm ----- %

%- solutions from midterm - %

f1 =[0.4681    0.4957
    0.3569   -0.1313]

f2 =[0.9000         0
    0.2459    0.8858 ]

C = [0.1;0]

% - compute states - % 

x(1:2,1)=[0;0];

for i = 1:1000
 x(:,i+1) = f2*x(:,i) + C*randn(1);
end

% - compute endo vars - %

for i = 1:1000
 y(:,i) = f1*x(:,i) ;
end

% - other endo vars go here - %
 
for i = 1:1000
 out(:,i) = x(1,i) + .3*x(2,i)+ (1-.3)*y(2,i) ;
end

std([out(1,100:1000)' y(1,100:1000)' y(2,100:1000)'])
corrcoef([out(1,100:1000)' y(1,100:1000)' y(2,100:1000)'])