Question

4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho, do )-min( (k, d)such that k > 0, d 0, and the proces s W t ▽k▽dX,-(1 B)a Find ko and do. For W, (with k = ko and d = do), express its acvf γw, in terms of acvfTY of { (ii) For process X, consider elimination of trend first BdXt is stationary} Let (k, , dı) = min{(k. d) such that k > 0, d > 0, and the process Vi := ▽d▽k X,-(1-Bd)(1-B)kXt is stationary} Are the values (k1,d) the same of different from (ko, do) found in ()? (iii) Based on your answers for (i) and (ii), what is your conclusion: to make X stationary, should one first eliminate seasonality, as in W, or first eliminate the trend as in V?

Answer 1

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