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The tail empirical process for long memory stochastic volatility sequences

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  • Kulik, Rafal
  • Soulier, Philippe

Abstract

This paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models. We show that such a process has dichotomous behaviour, according to an interplay between the Hurst parameter and the tail index. On the other hand, the tail empirical process with random levels never suffers from long memory. This is very desirable from a practical point of view, since such a process may be used to construct the Hill estimator of the tail index. To prove our results we need to establish new results for regularly varying distributions, which may be of independent interest.

Suggested Citation

  • Kulik, Rafal & Soulier, Philippe, 2011. "The tail empirical process for long memory stochastic volatility sequences," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 109-134, January.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:1:p:109-134
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    References listed on IDEAS

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    1. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    2. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    3. Einmahl, J.H.J., 1992. "Limit theorems for tail processes with application to intermediate quantile estimation," Other publications TiSEM 063e51b0-445d-4764-96a2-4, Tilburg University, School of Economics and Management.
    4. Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "A note on tightness," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 331-339, May.
    5. Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Papers 0706.1836, arXiv.org.
    6. Holger Drees, 2002. "Tail Empirical Processes Under Mixing Conditions," Springer Books, in: Herold Dehling & Thomas Mikosch & Michael Sørensen (ed.), Empirical Process Techniques for Dependent Data, pages 325-342, Springer.
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    Cited by:

    1. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    2. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    3. Rafal Kulik & Philippe Soulier, 2013. "Heavy tailed time series with extremal independence," Papers 1307.1501, arXiv.org, revised Oct 2014.
    4. Xiao Wang & Lihong Wang, 2024. "A tail index estimation for long memory processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 947-971, November.
    5. Rodríguez-Aguilar, Román & Cruz-Aké, Salvador & Venegas-Martínez, Francisco, 2014. "A Measure of Early Warning of Exchange-Rate Crises Based on the Hurst Coefficient and the Αlpha-Stable Parameter," MPRA Paper 59046, University Library of Munich, Germany.

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