(Solution) - A Suppose that E ut ut 1 ut 2 0 that var ut ut 1 ut 2 -(2025 Original AI-Free Solution)

Paper Details

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) = ?0/(1 - ?1).
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 ?1 + ?1 < 1 for a stationary GARCH(1,1) model.