3. Mixing

  1. Christian Francq1 and
  2. Jean-Michel Zakoïan1,2

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch3

GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

How to Cite

Francq, C. and Zakoïan, J.-M. (2010) Mixing, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch3

Author Information

  1. 1

    University Lille 3, Lille, France

  2. 2

    CREST, Paris, France

Publication History

  1. Published Online: 14 JUL 2010
  2. Published Print: 23 JUL 2010

ISBN Information

Print ISBN: 9780470683910

Online ISBN: 9780470670057

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Keywords:

  • β-mixing;
  • GARCH processes;
  • Markov chain;
  • Tweedie

Summary

This chapter discusses that under mild conditions GARCH processes are geometrically ergodic and β-mixing. These properties entail the existence of laws of large numbers and of central limit theorems and thus play an important role in the statistical analysis of GARCH processes. The chapter relies on the Markov chain techniques set out, for example, by Meyn and Tweedie.

Controlled Vocabulary Terms

generalized autoregressive conditional heteroskedasticity; Markov chain