Chapter 2. GARCH(p, q) Processes

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch2

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) GARCH(p, q) Processes, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch2

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:

  • univariate GARCH models - GARCH(p, q) processes;
  • autoregressive conditionally heteroscedastic (ARCH) models and key concept, of conditional variance;
  • GARCH models and GARCH processes - based on two conditional moments;
  • strict stationarity of GARCH models;
  • second-order stationarity - necessary and sufficient second-order stationarity conditions;
  • IGARCH(p, q) processes - model called integrated GARCH(p, q) or IGARCH(p, q) model;
  • ARCH(∞) representation;
  • class containing ARCH(q) process and GARCH(p, q) process;
  • ARCH(∞) representation of GARCH;
  • marginal distribution properties

Summary

This chapter contains sections titled:

  • Definitions and Representations

  • Stationarity Study

  • ARCH () Representation

  • Properties of the Marginal Distribution

  • Autocovariances of the Squares of a GARCH

  • Theoretical Predictions

  • Bibliographical Notes

  • Exercises