Suppose that a time series of stock returns {????????} can be represented using an ARCH(1)-M process ???????? = ????????2

???? + ????????, ???????? = ????????????????, and ????2

???? = ????0 + ????1????2

????−1, where the ????????

are iid Normal(0, 1).

(a) Derive the conditional and unconditional mean of the series.

(b) Show that the ARCH-in-mean effect makes the {????????} serially correlated and calculate the ACF ????????, ???? = 1, 2, … .