Suppose that { X t } is an ARIMA( p, d, q ) process satisfying the difference equations 1 answer below »

Suppose that {Xt} is an ARIMA(p, d, q) process satisfying the difference equations

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φ(B)(1 − B)dXtθ(B)Zt , {Zt} ∼ WN(02).

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Show that these difference equations are also satisfied by the process Wt=

XtA0 + A1+ · · · + Ad−1d−1, where A0, . . . , Ad−1 are arbitrary random variables.

 

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