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A Heavy-Tailed Distribution for ARCH Residuals with Application to Volatility Prediction

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  • Dimitris N. Politis

    () (Department of Mathematics, University of California)

Abstract

The quest for the `best' heavy-tailed distribution for ARCH/GARCH residuals appears to still be ongoing. In this connection, we propose a new distribution that arises in a natural way as an outcome of an implicit model. The challenging application of prediction of squared returns is also discussed; an optimal predictor is formulated, and the usefulness of the new distribution for prediction is demonstrated on three real datasets.

Suggested Citation

  • Dimitris N. Politis, 2004. "A Heavy-Tailed Distribution for ARCH Residuals with Application to Volatility Prediction," Annals of Economics and Finance, Society for AEF, vol. 5(2), pages 283-298, November.
    • Handle: RePEc:cuf:journl:y:2004:v:5:i:2:p:283-298
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    References listed on IDEAS

    as
    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    3. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. repec:ods:journl:v:6:y:2017:i:3:p:164-169 is not listed on IDEAS
    2. Hung, Jui-Cheng & Lee, Ming-Chih & Liu, Hung-Chun, 2008. "Estimation of value-at-risk for energy commodities via fat-tailed GARCH models," Energy Economics, Elsevier, vol. 30(3), pages 1173-1191, May.
    3. Dimitris N. Politis & Dimitrios D. Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Paper series 44_07, Rimini Centre for Economic Analysis.
    4. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    5. Su, Jung-Bin & Hung, Jui-Cheng, 2011. "Empirical analysis of jump dynamics, heavy-tails and skewness on value-at-risk estimation," Economic Modelling, Elsevier, vol. 28(3), pages 1117-1130, May.
    6. Politis, D N, 2006. "Can the Stock Market be Linearized?," University of California at San Diego, Economics Working Paper Series qt8th5q5hq, Department of Economics, UC San Diego.
    7. repec:rmk:rmkjrc:v:4:y:2017:i:1:p:43-49 is not listed on IDEAS
    8. J. A. Jiménez & V. Arunachalam & G. M. Serna, 2015. "Option Pricing Based On A Log–Skew–Normal Mixture," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-22, December.
    9. Chevallier, Julien & Ielpo, Florian, 2017. "Investigating the leverage effect in commodity markets with a recursive estimation approach," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 763-778.

    More about this item

    Keywords

    Heteroscedasticity; Kyrtosis; Maximum likelihood; Time series;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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