Chapter 7. Estimating GARCH Models by Quasi-Maximum Likelihood

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch7

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) Estimating GARCH Models by Quasi-Maximum Likelihood, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch7

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

SEARCH

Keywords:

  • estimating GARCH models by quasi-maximum likelihood (QML);
  • (QML) method, relevant for GARCH models;
  • conditional QML method - conditional on initial values;
  • asymptotic properties - of quasi-maximum likelihood estimator (QMLE);
  • application of method - to ARMA-GARCH model estimation;
  • ARCH(1) case - numerical evaluation of asymptotic variance;
  • nonstationary ARCH(1) - strict stationarity constraint, not satisfied in ARCH(1) case;
  • estimation of ARMA-GARCH models - by quasi-maximum likelihood;
  • proofs of asymptotic results;
  • asymptotic normality of QMLE of GARCH model - holding true under general conditions

Summary

This chapter contains sections titled:

  • Conditional Quasi-Likelihood

  • Estimation of ARMA-GARCH Models by Quasi-Maximum Likelihood

  • Application to Real Data

  • Proofs of the Asymptotic Results*

  • Bibliographical Notes

  • Exercises