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2. (a) For the following SARIMA(p, d, q) x (P, D, Q)s models, specify parameters p, d, q, P, D, Q and s, and write

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2. (a) For the following SARIMA(p, d, q) x (P, D, Q)s models, specify parameters p, d, q, P, D, Q and s, and write corresponding equations. It is helpful to first write equations in the form o(B) D(Bs) (1 - B)(1 - Bs)DX = 0(B)(B$) Zt, Zt ~ WN(0, oz), then proceed to rewrite the equations in the form that eliminates use of the backshift operator B. (i) SARIMA (1, 1, 0) x (1, 1, 2)6, (ii) SARIMA(0, 1, 1) x (0, 0, 3) 12, (iii) SARIMA(2, 1, 2) x (2, 0, 1) 4. (b) For the following processes {Xt}, identify SARIMA (p, d, q) x (P, D, Q)s model: (i) (1 - B12)2 Xt = (1 - 0.3B) Zt; (ii) Xt = 0.5Xt-6 + Zt; (iii) (1 - 0.8B)(1 + 0.5B4)Xt = (1 -1.5B) Zt. (c) You are given a time series model where PACF is zero except for lags 12 and 24. Which model will have this pattern

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