Question
4. Let {Yt} be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal component withperiod4,thatis,st
4. Let {Yt} be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal component withperiod4,thatis,st =st+4,t=1,2,...,andXt =a+bt+ct2+st+Yt. (i) For process X, eliminate seasonality first and trend second, that is, let (d0, s0) = min{(d, s) such that d, s 0, and the process Wt := dsXt = (1 B)d(1 Bs)Xt is stationary}. Find d0 and s0. (ii) For process X, consider elimination of trend first: Let (d1, s1) = min{(d, s) such that d, s 0, and the process Vt := sdXt = (1 Bs)(1 B)dXt is stationary}. Are the values (d1,s1) the same of different from (d0,s0) found in (i)? (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 ?
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