Consider the random walk with drift model xt = δ + xt−1 + wt, for t = 1,2,···, with x0 = 0, where wt is white noise with variance σw^2. t
(a) Show that the model can be written as xt = δt + wt. k=1
(b) Find the mean function and the autocovariance function of xt.
(c) Argue that xt is not stationary. t−1
(d) Show that rhox(t−1,t) = t → 1 as t → [infinity]. What is the implication of this result?
(e) Consider the process yt = xt − xt−1. Is the series {yt} stationary? Prove it.