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

Jonathan B. Hill and Artem Prokhorov

No 2015-03, Working Papers from University of Sydney Business School, Discipline of Business Analytics

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. We derive a higher order expansion for GEL with imbedded tail-trimming (GELITT), which reveals higher order bias and efficiency properties, available when the GARCH error has a finite second moment. Higher order asymptotics for GEL without tail-trimming requires the error to have moments of substantially higher order. We use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample. We also 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 expected shortfall estimation. Finally, we present a broad simulation study for GEL and GELITT, and demonstrate profile weighted expected shortfall for the Russian Ruble - US Dollar exchange rate. We show that tail-trimmed CUE-GMM dominates other estimators in terms of bias, mse and approximate normality.

Keywords: Russian Ruble; expected shortfall; efficient moment estimation; robust inference; heavy tails; tail trimming; GARCH; GEL (search for similar items in EconPapers)
Date: 2015-09-11
New Economics Papers: this item is included in nep-cis, nep-ecm, nep-ets, nep-ore and nep-rmg
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Citations: View citations in EconPapers (2)

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http://hdl.handle.net/2123/13795

Related works:
Journal Article: GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:syb:wpbsba:2123/13795

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