Least squares estimation for GARCH (1,1) model with heavy tailed errors

Arie Preminger and Giuseppe Storti

MPRA Paper from University Library of Munich, Germany

Abstract: GARCH (1,1) models are widely used for modelling processes with time varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a log-transform-based least squares estimator (LSE) for the GARCH (1,1) model. The asymptotic properties of the LSE are studied under very mild moment conditions for the errors. We establish the consistency, asymptotic normality at the standard convergence rate of square root-of-n for our estimator. The finite sample properties are assessed by means of an extensive simulation study. Our results show that LSE is more accurate than the quasi-maximum likelihood estimator (QMLE) for heavy tailed errors. Finally, we provide some empirical evidence on two financial time series considering daily and high frequency returns. The results of the empirical analysis suggest that in some settings, depending on the specific measure of volatility adopted, the LSE can allow for more accurate predictions of volatility than the usual Gaussian QMLE.

Keywords: GARCH (1; 1); least squares estimation; consistency; asymptotic normality. (search for similar items in EconPapers)
JEL-codes: C13 C15 C22 (search for similar items in EconPapers)
Date: 2014-01-17
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Working Paper: Least squares estimation for GARCH (1,1) model with heavy tailed errors (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:59082

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