a. Suppose that E(ut|ut-1, ut-2,...) = 0, that var(ut|ut-1, ut-2,...) follows the ARCH(l) model

and that the process for ut is stationary. Show that var(ut) = α0/(1 - α1).
b. Extend the result in (a) to the ARCH(p) model.
c. Show that

for a stationary ARCH(p) model.
d. Extend the result in (a) to the GARCH(1,1) model.
e. Show that α1 + ϕ1

o; = ag + auf-1-