Advanced Search
MyIDEAS: Login

Small Sample Estimation Bias in GARCH Models with Any Number of Exogenous Variables in the Mean Equation

Contents:

Author Info

  • Emma Iglesias
  • Garry Phillips

Abstract

In this article we show how bias approximations for the quasi maximum likelihood estimators of the parameters in Generalized Autoregressive Conditional Heteroskedastic (GARCH)(p, q) models change when any number of exogenous variables are included in the mean equation. The approximate biases are shown to vary in an additive and proportional way in relation to the number of exogenous variables, and they do not depend on the moments of the regressors under the correct specification of the model. This suggests a rule of thumb in testing for misspecification in GARCH models. We also extend the theoretical bias approximations given in Linton (1997) for the GARCH(1, 1). Because the expressions are not in closed form, we concentrate in detail, and for simplicity of interpretation, on the ARCH(1) model. At each stage, we check our theoretical results by simulation and generally, we find that the approximations are quite accurate for sample sizes of at least 50. We find that the biases are not trivial in some circumstances and we discuss how the bias approximations may be used, in practice, to reduce the bias. We also carry out simulations for the GARCH(1,1) model and show that the biases change as predicted by the approximations when the mean equation is augmented. Finally, we illustrate the usefulness of our approach for U.S. monthly inflation rates.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.tandfonline.com/doi/abs/10.1080/07474930903562551
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 30 (2011)
Issue (Month): 3 ()
Pages: 303-336

as in new window
Handle: RePEc:taf:emetrv:v:30:y:2011:i:3:p:303-336

Contact details of provider:
Web page: http://www.tandfonline.com/LECR20

Order Information:
Web: http://www.tandfonline.com/pricing/journal/LECR20

Related research

Keywords: Bias correction; GARCH; Quasi maximum likelihood;

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, vol. 1(4), pages 241-249, December.
  2. Emma M. Iglesias & Garry D.A. Phillips, 2004. "Multivariate Arch Models: Finite Sample Properties Of Ml Estimators And An Application To An Lm-Type Test," Working Papers. Serie AD 2004-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Iglesias, Emma M., 2006. "Higher-order asymptotic properties of QML in [beta]-ARCH and [mu]-ARCH models," Economics Letters, Elsevier, vol. 93(2), pages 261-266, November.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:30:y:2011:i:3:p:303-336. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.