9. Optimal Inference and Alternatives to the QMLE

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch9

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) Optimal Inference and Alternatives to the QMLE, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch9

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:

  • asymptotic normality;
  • maximum likelihood (ML);
  • optimal inference;
  • qausi-maximum likelihood (QML)

Summary

The maximum likelihood (ML) estimator provides the density f of the strong white noise (ηt ) and is assumed as known. This assumption is obviously very strong and the effect of the misspecification of f is examined. The ML estimator is studied in the (quite realistic) situation where f is misspecified. It is also seen that the so-called local asymptotic normality (LAN) property allows us to show the local asymptotic optimality of test procedures based on the ML. This chapter presents less standard estimators in order to address to some of the points. It focuses on the main principles of the estimation methods and do not give all the mathematical details. The estimation methods presented are less popular among practitioners than the qausi-maximum likelihood (QML) and LS methods, but each has specific features of interest.

Controlled Vocabulary Terms

inferential statistics