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.)

Please remove my post if this is not allowed/encouraged:

I understand this section's homework is testing our knowledge of the derivations of gamma and rho at different lags for a general linear process.  In my opinion NEAS gave us an alternating series to keep us on our toes with silly things such as sign errors.  While I am confident in my derivations, as the formulae are indeed straightfoward, I would like to check my finals answers against either the the back of the book (not an option) or the forum.  My answers will be rounded to three decimal places.

A.) gamma₀ = 9.375

B.) gamma₁ = 1.725

C.) gamma₂ = .345  -->  rho₂ = gamma₂/gamma₀

Lastly, does "one or two lines is sufficient for each part" mean only show some of your work?

RDH

(edited with revised gamma₂, guess why: sign error!)

[NEAS: Moving average processes often alternate: a positive residual in one period often causes a lower value in the next period. Sales of durable goods are an example. If sales are high one year, consumers may have lower demand the next year. If sales are low one year, the pent-up demand causes higher sales the next year.

The "one of two lines" is as you show. You need not explain the definitions of the gamma and rho parameters; just show the calculation.]