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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 A

Ergodicity, Martingales, Mixing

A.1 Ergodicity

A stationary sequence Is said to be ergodic If it satisfies the strong law of large numbers.

Definition A.1 (Ergodic stationary processes) A strictly stationary process (Zt)t2208_fmt2124_fmt realvalued, is said to be ergodic if and only if, for any Borel set B and any integer k,

bapp01ue001_fmt

with probability I.1

General transformations of ergodic sequences remain ergodic. The proof of the following result can be found, for instance, in Billingsley (1995, Theorem 36.4).

Theorem A.l If (Zt)t2208_fmt2124_fmt is an ergodic strictly stationary sequence and if(Yt)t2208_fmt2124_fmt is defined by

bapp01ue002_fmt

where f is a measurable function from to , then (Yt)t is also an ergodic strictly stationary sequence ...

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Publisher Resources

ISBN: 9780470683910