PSTAT 174/274, Fall 2021: Homework # 4. Note: In all problems, {Zt} ~ WN(0, oz) denotes white noise, and B denotes the backshift operator BXt = Xt-1. 1. For each of the models (1)-(3), write corresponding characteristic polynomials (z) and o(z). In other words, write models (1)-(3) as o(B)Xt = 0(B) Zt and specify polynomials 0(z) and o(z). For each, identify the model as a certain (S) ARIMA model and determine whether the model in invertible and stationary: (1) Xt = -0.2Xt-1+Zt-2Zt-1; (2) Xt = Xt-1+Zt-0.2Zt-1-0.7Zt-2; (3) Xt-Xt-3 = Zt+0.4Zt-1-0.45Zt-2