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GARCH Models
book

GARCH Models

by Christian Francq, Jean-Michel Zakoian
August 2010
Intermediate to advanced content levelIntermediate to advanced
504 pages
12h 59m
English
Wiley
Content preview from GARCH Models

Appendix D

Problems

Problem 1

The exercises are independent. Let (ηt) be a sequence of iid random variables satisfying Et) = 0 and Var(ηt) = 1.

Exercise 1: Consider, for all t 2208_fmt 2124_fmt, the model

bapp04ue001_fmt

where the constants satisfy ω > 0, αi ≥ 0,i = 1,…,q and βj ≥ 0, j = 1,…, p. We also assume that ηt is independent of the past values of 2208_fmtt. Let μ = Et|.

1. Give a necessary condition for the existence of E|2208_fmti|, and give the value of m = E|2208_fmtt|.

2. In this question, assume that p = q = 1.

(a) Establish a sufficient condition for strict stationarity using the representation

bapp04ue002_fmt

and give a strictly stationary solution of the model. It will be assumed that this condition is also necessary.

(b) Establish a necessary and sufficient condition for the existence of a second-order stationary solution. Compute the variance ...

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Publisher Resources

ISBN: 9780470683910