Chapter 8. Tests Based on the Likelihood

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch8

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) Tests Based on the Likelihood, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch8

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:

  • tests based on the likelihood;
  • testing IGARCH assumption, or a given GARCH model with infinite variance;
  • deriving tests - for nullity of coefficients;
  • test of second-order stationarity assumption;
  • critical region of stationarity test;
  • test of infinite variance assumption - and 11 stock market returns;
  • asymptotic distribution of QML;
  • standard tests modification;
  • diagnostic checking with portmanteau tests - checking adequacy of given time series model;
  • uniform integrability and continuity of second-order derivatives

Summary

This chapter contains sections titled:

  • Test of the Second-Order Stationarity Assumption

  • Asymptotic Distribution of the QML When θ0 is at the Boundary

  • Significance of the GARCH Coefficients

  • Diagnostic Checking with Portmanteau Tests

  • Application: Is the GARCH(1,1) Model Overrepresented?

  • Proofs of the Main Results

  • Bibliographical Notes

  • Exercises