%**********遞推增廣最小二乘估計算法(例2.2.1)**********
%**********cite為估值*********

M=600;
clear;
randn('seed',1);
e=sqrt(0.81)*randn(1,M+50);
y(1)=0;y(2)=0;

for t=1:M+20
    y(t+2)=-1.3*y(t+1)-0.4*y(t)+e(t+2)-1.1*e(t+1)+0.3*e(t);
end

fai(:,1)=[0,0,0,0]';cite(:,1)=[0;0;0;0];P=eye(4)*9999;
%********帶遺忘因子的最小二乘估計算法*********
for t=1:M
    ej(t)=y(t)-fai(:,t)'*cite(:,t);
    if t-1<=0
       fai(:,t+1)=[y(t),0,ej(t),0]';   
      else 
          fai(:,t+1)=[y(t),y(t-1),ej(t),ej(t-1)]';
    end
    cite(:,t+1)=cite(:,t)+P*fai(:,t+1)*(y(t+1)-fai(:,t+1)'*cite(:,t))/(1+fai(:,t+1)'*P*fai(:,t+1));
    P=P-(P*fai(:,t+1))*(P*fai(:,t+1))'/(1+fai(:,t+1)'*P*fai(:,t+1));
end
t=1:M;
a(1:M)=-1.3;
b(1:M)=-0.4;
subplot(2,2,1)
title('參數a的收斂圖');
plot(t,a(t),t,cite(1,t),'r');
subplot(2,2,2)
title('參數b的收斂圖');
plot(t,b(t),t,cite(2,t),'r');