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

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

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

 

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

 

 

For anyone that actually looks @ these forums for the fall course:

I was having the same problem as the quoted text...my issue was that I was not summing the geometric progression correctly...This is the case for both parts B & C.

The trick is that the first term cannot be part of the geometric sum as the sign is different. E.g. in Part B you get to:

phi*Var(et-1)) - phi^3*Var(et-2) - phi^5*Var(et-3)...

The proper sum is:

Var(et)*[phi - (phi^3 / (1-phi^2) ) ]

i.e. the first time is not part of the geometric sum.

Hope this helps someone.