A time series { X t } is differenced at lag 12, then at lag 1 to produce a zero-mean series { Y t }…

A time series {Xt} is differenced at lag 12, then at lag 1 to produce a zero-mean series {Yt} with the following sample ACF:

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a. Suggest a SARIMA model for {Xt} specifying all parameters.

b. For large n, express the one- and twelve-step linear predictors PnXn+1 and PnXn+12 in terms of Xt, t = −12,−11, . . . , n, and Yt − Yˆt, t = 1, . . . , n.

c. Find the mean squared errors of the predictors in (b).

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