6. Estimating ARCH Models by Least Squares

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

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch6

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) Estimating ARCH Models by Least Squares, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch6

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 models;
  • feasible generalized least squares (FGLS) estimator;
  • ordinary least squares (OLS)

Summary

The simplest estimation method for ARCH models is that of ordinary least squares (OLS). This estimation procedure has the advantage of being numerically simple, but has two drawbacks: (i) the OLS estimator is not efficient and is outperformed by methods based on the likelihood or on the quasi-likelihood; (ii) in order to provide asymptotically normal estimators, the method requires moments of order 8 for the observed process. An extension of the OLS method, the feasible generalized least squares (FGLS) method, suppresses the first drawback and attenuates the second by providing estimators that are asymptotically as accurate as the quasi-maximum likelihood under the assumption that moments of order 4 exist. The chapter discusses the unconstrained OLS and feasible generalized least squares (FGLS) estimators. It discusses how to take into account positivity constraints on the parameters.

Controlled Vocabulary Terms

autoregressive conditional heteroskedasticity; estimator; ordinary least squares