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Estimating the parameters of rare events

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  • Hsing, Tailen

Abstract

In this paper the estimation of certain parameters of the extreme order statistics of stationary observations is considered in a general framework. These parameters are resulted from dependence, and hence their inference is substantially different from similar considerations in the i.i.d. context. Variants of estimators that are functionals of the empirical 'cluster size' distribution are proposed, and such properties as consistency and asymptotic normality are studied. Special emphasis is given to estimating the extremal index.

Suggested Citation

  • Hsing, Tailen, 1991. "Estimating the parameters of rare events," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 117-139, February.
    • Handle: RePEc:eee:spapps:v:37:y:1991:i:1:p:117-139
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    Cited by:

    1. J. Sebastião & A. Martins & H. Ferreira & L. Pereira, 2013. "Estimating the upcrossings index," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 549-579, November.
    2. A. P. Martins & J. R. Sebastião, 2019. "Methods for estimating the upcrossings index: improvements and comparison," Statistical Papers, Springer, vol. 60(4), pages 1317-1347, August.
    3. Jose Olmo, 2015. "A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index," Econometrics, MDPI, vol. 3(3), pages 1-21, August.
    4. Segers, J.J.J., 2003. "Approximate Distributions of Clusters of Extremes," Other publications TiSEM 443e619d-453d-4a3c-b2f3-5, Tilburg University, School of Economics and Management.
    5. 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.
    6. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    7. Segers, J.J.J., 2003. "Approximate Distributions of Clusters of Extremes," Discussion Paper 2003-91, Tilburg University, Center for Economic Research.
    8. Olmo, José, 2005. "Testing the existence of clustering in the extreme values," UC3M Working papers. Economics we051809, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Segers, Johan, 2005. "Approximate distributions of clusters of extremes," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 330-336, October.
    10. Bücher, Axel & Jennessen, Tobias, 2022. "Statistical analysis for stationary time series at extreme levels: New estimators for the limiting cluster size distribution," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 75-106.
    11. Będowska-Sójka, Barbara & Echaust, Krzysztof & Just, Małgorzata, 2022. "The asymmetry of the Amihud illiquidity measure on the European markets: The evidence from Extreme Value Theory," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 78(C).
    12. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    13. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    14. Olmo, J., 2006. "A new family of estimators for the extremal index," Working Papers 06/01, Department of Economics, City University London.
    15. John Galbraith & Serguei Zernov, 2009. "Extreme dependence in the NASDAQ and S&P 500 composite indexes," Applied Financial Economics, Taylor & Francis Journals, vol. 19(13), pages 1019-1028.

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