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:

  • ARCH effect;
  • ARMA-GARCH Model;
  • GARCH Process;
  • Lagrange multiplier (LM) test;
  • noncorrelation

Summary

This chapter discusses the problem of selecting an appropriate GARCH or ARMA-GARCH model for given observations X1, . ., Xn of a centered stationary process. The price variation process, X = (Xt ), should thus constitute a martingale difference sequence, and should coincide with its innovation process, ε = (εt). It addresses the test of this property, at least a consequence of it: absence of correlation. The problem is far from trivial because standard tests for noncorrelation are actually valid under an independence assumption. Such an assumption is too strong for GARCH processes which are dependent though uncorrelated. It discusses identification of the orders (P, Q) and (p, q). The chapter considers tests of the ARCH effect. It derives the general form of the Lagrange multiplier (LM) test and then presents an LM test for conditional homoscedasticity.

Controlled Vocabulary Terms

ARMA model; autoregressive conditional heteroskedasticity; generalized autoregressive conditional heteroskedasticity