4. Temporal Aggregation and Weak GARCH Models

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch4

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) Temporal Aggregation and Weak GARCH Models, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch4

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:

  • semi-strong GARCH models;
  • temporal aggregation;
  • weak GARCH

Summary

This chapter considers invariance properties of the class of GARCH processes with respect to time transformations frequently encountered in econometrics. It is seen that, to obtain stability properties, a wider class of GARCH-type models, called weak GARCH is introduced based on the L2 structure of the squared returns. Temporal aggregation arises when the frequency of data generation is lower than that of the observations so that the underlying process is only partially observed. The class of semi-strong GARCH models is not large enough to include all processes obtained by temporal aggregation of strong GARCH. The chapter shows that the weak GARCH class of models is stable by temporal aggregation. Before that, it examines the GARCH(1, 1) model, for which the solution is more explicit.

Controlled Vocabulary Terms

generalized autoregressive conditional heteroskedasticity; simple aggregate iindex