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

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

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

A. Suppose that E(ut|ut-1, ut-2,...) = 0, that var(ut|ut-1, ut-2,...)

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

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Introduction to Econometrics

ISBN: 978-0133595420

3rd edition

Authors: James H. Stock, Mark W. Watson

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