Question: Consider a time series model: Xt = 6+ Xt-1+ wt, t=1,2, ..., and x0 = 0, ( 4) where we are i.i.d. with zero mean

Consider a time series model: Xt = 6+ Xt-1+ wt, t=1,2, ..., and x0 = 0, ( 4) where we are i.i.d. with zero mean and variance o2. (a) Show that Xt = St + _k=1 Wk (b) Calculate the mean u(t) := EXt] and the autocovariance (t, s) := Cov(Xt, Xs) = EL( Xt - M(t) ) ( Xs - M(s) ) ]. (c) Calculate the autocorrelation p(s, t) := 7 (t, s ) What is the limit of p(t - 1, t) when Vy(t,t ) 7(s, s) t - co? What does this imply on the predictive power of Xt-1 on Xt when t is large? (d) Is Xt weakly stationary? (e) Is AXt := Xt - Xt_1 weakly stationary

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