PSTAT 174/274, Fall 2021: Homework # 4. Note: In all problems, { Z.} ~ WN(0, o- ) denotes white noise, and B denotes the backshift operator BX, = X-1. 1. For each of the models (1)-(3), write corresponding characteristic polynomials 0(z) and d(z). In other words, write models (1)-(3) as o( B)X, -0(B) Z, 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) X, = -0.2X1-1+21-2Z-1; (2) X. = X -1+Z-0.2Z,-1-0.721-2; (3) X.-X-3 = Z.+0.4Zz-1-0.45Zz-2