Chapter 5. Identification

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch5

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) Identification, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch5

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:

  • statistical inference - autocorrelation check for white noise;
  • problem of selecting appropriate GARCH or ARMA-GARCH model - for given observations X1, …, Xn of centered stationary process;
  • autocorrelation check for white noise;
  • sample autocorrelations (SACRs);
  • behavior of sample autocorrelations of GARCH process;
  • standard portmanteau test - checking that data is a realization of a strong white noise, Ljung and Box (1978);
  • sample partial autocorrelations (SPACs) - SPACs and their significance bounds;
  • identifying ARMA orders of ARMA-GARCH;
  • order determination, based on sample and partial autocorrelations in mixed ARMA(P, Q) model - not an easy task;
  • Box–Jenkins methodology for ARMA models - also adapted to GARCH(p, q) models

Summary

This chapter contains sections titled:

  • Autocorrelation Check for White Noise

  • Identifying the ARMA Orders of an ARMA-GARCH

  • Identifying the GARCH Orders of an ARMA-GARCH Model

  • Lagrange Multiplier Test for Conditional Homoscedasticity

  • Application to Real Series

  • Bibliographical Notes

  • Exercises