Consider the time series xt = 1 + 2t + wt, where 1 and 2 are known constants and wt is a white noise process

Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w.

(a) Determine whether xt is stationary.

(b) Show that the process yt = xt − xt−1 is stationary

(c) Show that the mean of the moving average vt = 1 2q + 1 Xq j=−q xt−j is β1+β2t, and give a simplified expression for the autocovariance function.