erc/metu
INTERNATIONAL CONFERENCE IN ECONOMICS  IV
September 13-16, 2000, Ankara

Small Sample Estimation Bias in ARCH Models

Emma M. Iglesias (University of Exeter, UK)
Garry D. A. Phillips (Cardiff University, UK)

Abstract

In this paper we use the Cox and Snell (1986) approach to find expressions for the second order biases of the Quasi-Maximum Likelihood Estimators (QMLEs) of the parameters in an ARCH(1) model with an unknown intercept in the mean equation. The results are then extended to examine the consequences of the introduction of an exogenous variable. While our results confirm the findings in the work by Engle, Hendry and Trumble (1985) and Linton (1997) for the parameter of the lagged squared residual in the ARCH process, we find that in the case of the intercept there is a bias of order (T-1), which is in contradiction to Linton (1997). However, the bias we find is smaller than that given in the paper by Engle et al (1985). Finally, we give a general matrix formula for computing the biases of the QMLEs of the AR(p)-ARCH(1) model with known mean. The results are then specialised to the case of the simple AR(1)-ARCH(1) model.

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