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

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  • Hill, Jonathan B.
  • Prokhorov, Artem
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.

Suggested Citation

  • Hill, Jonathan B. & Prokhorov, Artem, 2015. "GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference," Working Papers 2015-03, University of Sydney Business School, Discipline of Business Analytics.
    • Handle: RePEc:syb:wpbsba:2123/13795
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    2. Manabu Asai & Mike K. P. So, 2021. "Quasi‐maximum likelihood estimation of conditional autoregressive Wishart models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 271-294, May.
    3. Valentyn Panchenko & Artem Prokhorov, 2011. "Efficient estimation of parameters in marginals in semiparametric multivariate models," Working Papers 11001, Concordia University, Department of Economics.
    4. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    5. Lisa Crosato & Luigi Grossi, 2019. "Correcting outliers in GARCH models: a weighted forward approach," Statistical Papers, Springer, vol. 60(6), pages 1939-1970, December.
    6. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    7. Yuya Sasaki & Yulong Wang, 2020. "Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators," Papers 2006.02541, arXiv.org, revised Sep 2020.
    8. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
    9. Jihyun Kim & Nour Meddahi, 2020. "Volatility Regressions with Fat Tails," Post-Print hal-03142647, HAL.

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    More about this item

    Keywords

    Russian Ruble; expected shortfall; efficient moment estimation; robust inference; heavy tails; tail trimming; GARCH; GEL;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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