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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. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. 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.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Citations

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    Cited by:

    1. Dimitris Politis & Dimitrios Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Papers 0005, University of Peloponnese, Department of Economics.
    2. Halkos, George & Tsirivis, Apostolos, 2019. "Using Value-at-Risk for effective energy portfolio risk management," MPRA Paper 91674, University Library of Munich, Germany.
    3. Panos Pouliasis & Ioannis Kyriakou & Nikos Papapostolou, 2017. "On equity risk prediction and tail spillovers," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 22(4), pages 379-393, October.
    4. 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.
    5. Laporta, Alessandro G. & Merlo, Luca & Petrella, Lea, 2018. "Selection of Value at Risk Models for Energy Commodities," Energy Economics, Elsevier, vol. 74(C), pages 628-643.
    6. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    7. 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.
    8. Yoon Hong & Ji-chul Lee & Guoping Ding, 2017. "Volatility Clustering, New Heavy-Tailed Distribution and the Stock Market Returns in South Korea," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 6(3), pages 164-169, September.
    9. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
    10. Dimitrios Thomakos & Johannes Klepsch & Dimitris N. Politis, 2020. "Model Free Inference on Multivariate Time Series with Conditional Correlations," Stats, MDPI, vol. 3(4), pages 1-26, November.
    11. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Value-at-risk methodologies for effective energy portfolio risk management," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 197-212.
    12. 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.
    13. 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.
    14. Michael Day & Mark Diamond & Jeff Card & Jake Hurd & Jianping Xu, 2017. "GARCH model and fat tails of the Chinese stock market returns - New evidences," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 43-49.
    15. Huang, Yu-ting & Bai, Yu-long & Yu, Qing-he & Ding, Lin & Ma, Yong-jie, 2022. "Application of a hybrid model based on the Prophet model, ICEEMDAN and multi-model optimization error correction in metal price prediction," Resources Policy, Elsevier, vol. 79(C).
    16. 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.
    17. 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.

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    More about this item

    Keywords

    Heteroscedasticity; Kyrtosis; Maximum likelihood; Time series;
    All these keywords.

    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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