Consider a process consisting of a linear trend with an additive noise term consisting of independent random variables wt with zero means and variances 2

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 w, 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).