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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)

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    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.

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    File URL: http://www.aeconf.net/Articles/Nov2004/aef050206.pdf
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    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 5 (2004)
    Issue (Month): 2 (November)
    Pages: 283-298

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    Handle: RePEc:cuf:journl:y:2004:v:5:i:2:p:283-298
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    Keywords: Heteroscedasticity; Kyrtosis; Maximum likelihood; Time series;

    Find related papers by 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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    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.
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    Cited by:

    1. 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.
    2. Dimitris N. Politis & Dimitrios D. Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Paper Series 44_07, The Rimini Centre for Economic Analysis.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Politis, Dimitris N & Thomakos, Dimitrios D, 2008. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," University of California at San Diego, Economics Working Paper Series qt982208kx, Department of Economics, UC San Diego.

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