Provide all steps to the problem: time series

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1 Problem 1 { Order CI differencing removes an order d deterministic polynomial trend). Suppose int = [Lt + Zt (1) With ,qu being a dth degree polynomial in t, Mt=60+61t+"'+5dtda (2) Where ,80, - - 3/901 are constants and {2t} is a zeromean stationary time series With autocovariance function 7201.). (a) Show that {Vzt} is a zeromean stationary time series. (b) For d = 1 (,81 a 0), show that {m} is not stationary but Va is stationary. (0) Suppose d = k + 1 (13k+1 a 0) for some positive integer 16. Show that th 2 [L + it, (3) Where [it is a degree is polynomial in t and it is a zeromean stationary time series. (d) Use induction to show that for a general d, met is stationary for m 2 d and nonstationary for 0 g m