Suppose that we have an ARCH(2) model for financial returns ut = tt 2 t = 0 + 1u 2 t1 + 2u 2 t2 t iid N (0, 1) where t is independent of t , 1 0, 2 0 and 0 > 0. We assume that {ut} is weakly stationary.

Derive the unconditional mean and variance of {ut}.