- Consider Yt Pyt 1 Ut Where U Is White Noise Such That E U Ft 1 0 With F Is The O Algebra Generated By Yt Yt 1 1 (37.64 KiB) Viewed 20 times
legiblly
Consider Yt = pyt-1 + Ut, where {U} is white noise such that E[U₁Ft-1] =0 with F, is the o-algebra generated by Yt, Yt-1,..., and Var (U₂) = ² <∞o for all t. We assume that p < 1 and that (Y) is strictly stationary and ergodic. (a) Find the OLS estimator of p. p. (b) Show that the process (Y₁-1 U₂) is a martingale difference sequence with respect to Ft-1 (i.e., show that E[Y₁-1Ut|Ft-1] = 0). 1 (e) Show that is consistent for p. (d) Derive the asymptotic distribution of √T(-p). For this question, make assumptions needed to use some appropriate asymptotic tools, if necessary.