GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference

30 Pages Posted: 8 Oct 2011 Last revised: 15 Jul 2013

See all articles by Jonathan B. Hill

Jonathan B. Hill

University of North Carolina (UNC) at Chapel Hill – Department of Economics

Artem Prokhorov

Concordia University, Quebec - Department of Economics

Date Written: July 8, 2013

Abstract

We construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to non-leverage points. Finally, we present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to the estimation of a conditionally heteroscedastic asset's expected shortfall.

Keywords: GEL, GARCH, tail trimming, heavy tails, robust inference, efficient moment estimation

Suggested Citation

Hill, Jonathan B. and Prokhorov, Artem, GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference (July 8, 2013). Available at SSRN: https://ssrn.com/abstract=1940133 or http://dx.doi.org/10.2139/ssrn.1940133

Jonathan B. Hill (Contact Author)

University of North Carolina (UNC) at Chapel Hill – Department of Economics ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

Artem Prokhorov

Concordia University, Quebec - Department of Economics ( email )

1455 de Maisonneuve Blvd. W.
Montreal, Quebec H3G 1MB
Canada

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