1. Consider an AR(1) regression model with stationary data: where a and p (p| < 1) are unknown parameters, ut is i.i.d (0,0). Suppose that the data is stationary. (a) Let u = E(yt), show that = a/(1-p) (you need to show your derivations leading to this result). (b) Derive Var (yt) =? (in terms of p and o). Yt = a + pyt-1 + Ut obtain t de f Hint: You can re-write the model in a de-mean form, i.e., let yt Ytu and (explain how to) pt1+ut. What is the relationship between Var(yt) and Var(t) = Var(yt )? = (t = 1,..., n) (c) Discuss how can you estimate a and p given data {yt}?=1 (d) Discuss how can you test Ho: p= 0.8 against H: p0.8. You need to discuss how to compute your test statistic, the distribution of your test statistic under Ho and your decision rule, i.e., under what condition you reject Ho. Hint: Let 3 = (a). (). Explain your definition of Y and X. and B = ( The model can be written in a matrix form as Y = XB+u.