TIME SERIES QUESTION - THANKS :)

Question 3 [30 marks]. Consider the following model Xt - 0.5Xt-1 - 0.2Xt-2 = Zt + 0.4Zt-1 where { Zt} is a Gaussian white noise process with mean 0 and variance o2. (a) What SARIMA model is this? [6] (b) Is this model causal? [3] (c) Use the method of coefficients matching and express this model in the form of a linear process Xt = _jov; Zt ; with vo = 1. Find an explicit formula for v; without any recursions. [17] (d) Note that in order for Xt = _ ; Zt-; to hold in terms of mean square convergence, we need _ _ lu;|