E
Edward Smith
Member
On this question, I can see that for Model X, we can derive an estimate for a1 by calculating:
Autocov(0)=Cov(a0+a1yt-1+et,yt) = a1*autocov(1) + sigma^2
Autocov(1)=Cov(a0+a1yt-l+et,yt-1) = a1*autocov(0), thus a1 = autocov(1)/autocov(0) = r1
However, why can we not solve by:
Autocov(0)=Cov(a0+a1yt-1+et,a0+a1yt-1+et) = a1^2*autocov(0) + sigma^2
Autocov(1)=Cov(a0+a1yt-1+et,a0+a1yt-2+et-1) = a1^2*autocov(1)... here we get a1^2 = autocov(1)/autocov(1) which is not the same as above?
Autocov(0)=Cov(a0+a1yt-1+et,yt) = a1*autocov(1) + sigma^2
Autocov(1)=Cov(a0+a1yt-l+et,yt-1) = a1*autocov(0), thus a1 = autocov(1)/autocov(0) = r1
However, why can we not solve by:
Autocov(0)=Cov(a0+a1yt-1+et,a0+a1yt-1+et) = a1^2*autocov(0) + sigma^2
Autocov(1)=Cov(a0+a1yt-1+et,a0+a1yt-2+et-1) = a1^2*autocov(1)... here we get a1^2 = autocov(1)/autocov(1) which is not the same as above?