Finite sample theory of QMLE in ARCH models with dynamics in the mean equation

Iglesias, Emma M. and Phillips, Garry David Alan 2008. Finite sample theory of QMLE in ARCH models with dynamics in the mean equation. Journal of Time Series Analysis 29 (4) , pp. 719-737. 10.1111/j.1467-9892.2008.00582.x

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Abstract

We provide simulation and theoretical results concerning the finite-sample theory of quasi-maximum-likelihood estimators in autoregressive conditional heteroskedastic (ARCH) models when we include dynamics in the mean equation. In the setting of the AR(q)–ARCH(p), we find that in some cases bias correction is necessary even for sample sizes of 100, especially when the ARCH order increases. We warn about the existence of important biases and potentially low power of the t-tests in these cases. We also propose ways to deal with them. We also find simulation evidence that when conditional heteroskedasticity increases, the mean-squared error of the maximum-likelihood estimator of the AR(1) parameter in the mean equation of an AR(1)-ARCH(1) model is reduced. Finally, we generalize the Lumsdaine [J. Bus. Econ. Stat. 13 (1995) pp. 1–10] invariance properties for the biases in these situations.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Business (Including Economics)
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Uncontrolled Keywords:	AR-ARCH models ; Quasi-maximum likelihood ; Bias correction
Publisher:	Wiley Blackwell
ISSN:	0143-9782
Last Modified:	19 Oct 2019 02:29
URI:	https://orca.cardiff.ac.uk/id/eprint/18407

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