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

Emma Iglesias and Garry Phillips

Econometric Reviews, 2011, vol. 30, issue 3, 303-336

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.

Keywords: Bias correction; GARCH; Quasi maximum likelihood (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/07474930903562551 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:emetrv:v:30:y:2011:i:3:p:303-336

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/LECR20

DOI: 10.1080/07474930903562551

Access Statistics for this article

Econometric Reviews is currently edited by Dr. Essie Maasoumi

More articles in Econometric Reviews from Taylor & Francis Journals
Bibliographic data for series maintained by ().