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CS2 September 2022 - Q6 i)

A

Alex14

Made first post
Hello,

Could somebody please provide a more explicit solution to Q6i in the Sep 2022 paper?

In the examiner's report it says "Suppose we have shown that e_t = x_t + Sum(1,t-1)[(-b)^i x_t-i]". Why is that given?

Thanks,
Alex
 
Hi Alex
Did you purchase the ASET for CS2, that gives a fuller explanation?
This was a tricky question.
We need to show the likelihood in terms of b, if we rearrange the defining equation as e_t=X_t-be_t-1 and repeatedly substitute in we get to that formula.
We need it as we are finding the likelihood of the error terms, which are normally distributed N(0,sigma^2).
Thanks
Andrea
 
Thank you Andrea,

I'm re-taking this exam, so I only have the ASET up to April 2022.

I've managed to prove e_t = x_t + Sum(1,t-1)[(-b)^i x_t-i] by repeatedly substituting as you mentioned above.

Thanks a lot for your help.

Alex
 
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