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Testing the existence of clustering in the extreme values

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  • Olmo, José

Abstract

This paper introduces an estimator for the extremal index as the ratio of the number of elements of two point processes defined by threshold sequences un, vn and a partition of the sequence in different blocks of the same size. The first point process is defined by the sequence of the block maxima that exceed un. This paper introduces a thinning of this point process, defined by a threshold vn with vn > un, and with the appealing property that under some mild conditions the ratio of the number of elements of both point processes is a consistent estimator of the extremal index. The method supports a hypothesis test for the extremal index, and hence for testing the existence of clustering in the extreme values. Other advantages are that it allows some freedom to choose un, and it is not very sensitive to the choice of the partition. Finally, the stylized facts found in financial returns (clustering, skewness, heavy tails) are tested via the extremal index, in this case for the DaX returns

Suggested Citation

  • 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.
    • Handle: RePEc:cte:werepe:we051809
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    References listed on IDEAS

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    1. Laurens de Haan, 1976. "Sample extremes: an elementary introduction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 30(4), pages 161-172, December.
    2. Hsing, Tailen, 1991. "Estimating the parameters of rare events," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 117-139, February.
    3. de Haan, Laurens, 1976. "Sample Extremes: An Elementary Introduction," Econometric Institute Archives 272130, Erasmus University Rotterdam.
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    Cited by:

    1. Nikolaus Hautsch & Rodrigo Herrera, 2020. "Multivariate dynamic intensity peaks‐over‐threshold models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 248-272, March.

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