Suppose that annual sales (in millions of dollars) of the Acme Corporation follow the AR(2) model Yt = 5 + 1.1Yt-1 – 0.5Yt-2 + Et with σ ² _e = 2.

(a). If sales for 2005, 2006, and 2007 were $9 million, $11 million, $10 million, respectively, forecast sales for 2008 and 2009.

(b). Show that 01 = 1.1 for this model.

(c). Calculate 95% prediction limits for your forecast in part (a) for 2008. Do the same for 2009.

(d). If sales in 2008 turn out to be $12 million, update your forecast for 2009.