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Tail index estimation in the presence of long-memory dynamics

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  • McElroy, Tucker
  • Jach, Agnieszka

Abstract

Most tail index estimators are formulated under assumptions of weak serial dependence, but nevertheless are applied in practice to long-range dependent time series data. This issue arises because for many time series found in teletraffic and financial econometric applications, both heavy tails and long memory are prevalent features. For a certain class of Heavy-Tail Long-Memory (HTLM) processes, McElroy and Politis (2007a) and Jach et al. (2011) found that the probabilistic behavior of the sample mean depends delicately on the interplay of the tail index and the long memory parameter. In contrast, results in Kulik and Soulier (2011) indicate that the sample quantiles for a related HTLM process are unaffected by long-range dependence. Motivated by these results, we undertake an extensive numerical study to compare the finite-sample performance of several tail index estimators–both those based on sample quantiles, such as the Hill and DEdH (Hill (1975) and Dekkers et al. (1989)) as well as those based on moments, e.g. Meerschaert and Scheffler (1998)–in the HTLM context. Our results largely confirm and expand those of Kulik and Soulier (2011), in that the Hill and DEdH estimators perform well despite the presence of long memory.

Suggested Citation

  • McElroy, Tucker & Jach, Agnieszka, 2012. "Tail index estimation in the presence of long-memory dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 266-282.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:266-282
    DOI: 10.1016/j.csda.2011.07.018
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    References listed on IDEAS

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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    2. Agnieszka Jach & Tucker McElroy & Dimitris N. Politis, 2012. "Subsampling inference for the mean of heavy‐tailed long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 96-111, January.
    3. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    4. T. Rachev, Svetlozar & Samorodnitsky, Gennady, 2001. "Long strange segments in a long-range-dependent moving average," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 119-148, May.
    5. 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.
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    2. Giuseppe Arbia & Riccardo Bramante & Silvia Facchinetti, 2020. "Least Quartic Regression Criterion to Evaluate Systematic Risk in the Presence of Co-Skewness and Co-Kurtosis," Risks, MDPI, vol. 8(3), pages 1-14, September.

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