An Almost Closed Form Estimator for the EGARCH Model

28 Pages Posted: 1 Sep 2012 Last revised: 27 Apr 2015

See all articles by Christian Hafner

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics; Tinbergen Institute

Oliver B. Linton

University of Cambridge

Date Written: April 27, 2015

Abstract

The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference is usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.

Keywords: Autocorrelations, Generalized Error Distribution, Method of Moments Estimator, Newton-Raphson

JEL Classification: C12, C13, C14

Suggested Citation

Hafner, Christian and Linton, Oliver B., An Almost Closed Form Estimator for the EGARCH Model (April 27, 2015). Available at SSRN: https://ssrn.com/abstract=2139516 or http://dx.doi.org/10.2139/ssrn.2139516

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics ( email )

Voie du Roman Pay
34 B-1348 Louvain-La-Neuve, 1348
Belgium

Tinbergen Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

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