3. One differences a time series Xt at lag 6, and at lag 1 to produce a zero-mean times series Y't with the following sample statistics: p(6k) ~ (0.9)k, k = 0, +1, 12, ..., p(6k + 1) ~ (0.4) (0.9)k, k = 0, +1, 12, ..., p(h) ~ 0, otherwise, and 7(0) = 20. (a) Suggest a SARIMA model for Xt. Justify your answer, and specify all the parameters in the model. (10 pt) (b) For large n, find the linear predictor PXn+1 in terms of Xt, t = -6, ...,n, and Yn - Yn. (5 pt) (c) Find the mean squared error of the prediction in part (b). (5 pt)