Neas-Seminars

TS Module 5: Stationary processes HW


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By NEAS - 12/4/2009 6:07:23 AM

TS Module 5: Stationary processes HW

 

(The attached PDF file has better formatting.)

 

Homework assignment: general linear process

 

A time series has the form Yt = åt + ö × åt-1 – ö2 × åt-2 + ö3 × åt-3 – …

 

The plus and minus signs alternate.  ö = 0.2 and ó2e = 9.

 


A.     What is ã0, the variance of Yt? Show the derivation.

B.     What is ã1, the covariance of Yt and Yt-1? Show the derivation.

C.    What is ñ2, the correlation of Yt and Yt-2? Show the derivation.

 

(Show the algebra for the derivations. One or two lines is sufficient for each part.)

 

 
By 292lu - 5/9/2015 9:07:52 PM

I don't agree with the answer to A posted here. It looks like you did 9/(1-.2^2) which would be the answer if it weren't an alternating series (i.e if it was 9*(1+.2^2+.2^4+...). However, this series is 9*(1+.2^2-.2^4+.2^6+...) I think, which shouldn't converge to the same value, right? I'm not sure if there is an exact formula for solving the alternating series, but I summed the first several terms and rounded and I get a different answer.

Edit: Never mind, I get it. Forgetting how to get a variance!