Consider a process consisting of a linear trend with an additive noise term consisting of independent random variables wt with zero means and variances σ2 , that is,
xt = β0 + β1t + wt,
where β0, β1 are ﬁxed constants.
(a) Prove xt is nonstationary.
(b) Prove that the ﬁrst diﬀerence series ∇xt = xt − xt−1 is stationary by ﬁnding its mean and autocovariance function.
(c) Repeat part (b) if wt is replaced by a general stationary process, say yt, with mean function µy and autocovariance function γy (h).