%Store oil prices in oil(81,1) using import data
%Autoregressive order 1
[para,conf]=regress(oil(2:41),[ones(40,1) oil(1:40)])
a=para(2);b=para(1);p=zeros(81,0);
SE=0.0; %Square Error
for i=46:81
    p(i,1)=oil(i-5);
    for j=1:5
        p(i,1)=a*p(i,1)+b;
    end
    SE=SE+(p(i,1)-oil(i))^2;
end
SE
hold off;
plot(p(46:81),'.-r');
hold on;
plot(oil(46:81));

%Autoregressive order 2
[para,conf]=regress(oil(3:41),[ones(39,1) oil(2:40) oil(1:39)])
a=para(2:3);b=para(1);p=zeros(81,0);
F=[a';1 0];b=[b;0];R=[1 0;0 1];K=zeros(2,1);
for i=0:4
    K=K+R*b;
    R=R*F;
end
R=R*F;
SE=0.0; %Square Error
for i=46:81
    yn=[oil(i-5);oil(i-6)];
    p(i,1)=K(1,1)+[1 0]*R*yn;
    SE=SE+(p(i,1)-oil(i))^2;
end
SE
hold on;
plot(p(46:81),'.-g');

%Autoregressive order 3
[para,conf]=regress(oil(4:41),[ones(38,1) oil(3:40) oil(2:39) oil(1:38)])
a=para(2:4);b=para(1);p=zeros(81,0);
F=[a';eye(2) zeros(2,1)];b=[b;0;0];R=eye(3);K=zeros(3,1);
for i=0:4
    K=K+R*b;
    R=R*F;
end
R=R*F;
SE=0.0; %Square Error
for i=46:81
    yn=[oil(i-5);oil(i-6);oil(i-7)];
    p(i,1)=K(1,1)+[1 0 0]*R*yn;
    SE=SE+(p(i,1)-oil(i))^2;
end
SE
hold on;
plot(p(46:81),'.-b');