Chapter 3. Mixing

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch3

Book Title

GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

Additional Information

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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CHAPTER TOOLS

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Keywords:

  • mixing;
  • GARCH processes, geometrically ergodic and β-mixing;
  • Markov Chains with continuous state space;
  • invariant probability - also called stationary probability;
  • small sets and aperiodicity;
  • geometric ergodicity and mixing;
  • two ergodicity criteria - simple criteria on transition kernel;
  • mixing properties of GARCH processes;
  • Lebesgue dominated convergence theorem - effective way to show geometric ergodicity of Markov processes;
  • geometric ergodicity and mixing properties of GARCH(p, q) processes

Summary

This chapter contains sections titled:

  • Markov Chains with Continuous State Space

  • Mixing Properties of GARCH Processes

  • Bibliographical Notes

  • Exercises

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