Ouch, zarito.  I really don't like that the textbook highlights formulae for specific problems, and not general cases.  It is fairly straightforward to derive the general case from 5.1.4 and 5.1.5.  The problem does ask to show the derivations though, so I began from 5.1.2 and 5.1.3 on the previous page.  Taking a look at 5.1.4, we know beta = 3, but there is an 8 and a 9 in the formula.

So, ask yourself, how does one derive 8 and 9 from 3?

8 = 3^2 - 1

9 = 3^2

This should very simply solve your dilema.  If you would like to follow the 5.1.2 and 5.1.3 route, it involves geometic series, which also simplify very nicely.  Best of luck!

RDH

Should we assume that Y_t=0 for t<1?  You made it clear in the practice problems that this condition must be given in order for the variance to be defined, but then did not give us this condition in the homework.

[NEAS: Yes; use the same assumptions as in textbook on page 89, equations 5.1.4 and 5.1.5.]

I said this in the module 8 section.  The homework for module 9 references material in module 8.  Now I am a few pages into the module 9 reading and it looks like you can answer the module 8 homework with the module 9 reading.  Am I off base with this?

[NEAS: Both homework assignments deal with ARIMA processes. Answer them after working through both modules.]