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

ut = tt

^2 t = 0 + 1u^2 t1 + 2u^2 t2

et iid N (0, 1)

where et is independent of t , 1 0, 2 0 and 0 > 0. We assume that {ut} is weakly stationary.

) Suppose that we have estimated the ARCH(2) model and obtained the parameter estimates: 0 = 1, 1 = 0.5, and 2 = 0.1. Assume that u^2 T = 1, and u^2 T 1 = 0 are observed. Denote by ^2 T +h|T the h-step-ahead forecast of the conditional variance. Compute the one- and two-step-ahead forecasts of the conditional variance ^2 t