Suppose that we have an ARCH(2) model for financial returns

Problem 2 (25 marks). Suppose that we have an ARCH(2) model for nancial returns \"at 5:0: 2 at an + 0:111:24 + 021134 63 ~ iid NW, 1) where at is independent of at, on 2 0,0:2 2 {J and do > 0. We assume that {m} is weakly stationary. a) Derive the uneonditional mean and variance of {H1}. [10 marks] 13) Derive a condition on the parameters which ensures weak stationarity of the {m} pro- cess. [5 marks] c) Suppose that we have estimated the ARCH(2) model and obtained the parameter estimates: an = 1, e; = 0.5, and a2 = 0.1. Assume that 113}. = 1, and uh = o are observed. Denote by 0;.\"13. the h-step-ahead forecast of the conditional variance. Compute the one and twostepahead forecasts of the conditional variance of. [10 marks]