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Kernel Methods for Small Sample and Asymptotic Tail Inference for Dependent, Heterogeneous Data


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  • Jonathan Hill

    (Department of Economics, Florida International University)


This paper considers tail shape inference techniques robust to substantial degrees of serial dependence and heterogeneity. We detail a new kernel estimator of the asymptotic variance and the exact small sample mean-squared-error, and a simple representation of the bias of the B. Hill (1975) tail index estimator for dependent, heterogeneous data. Under mild assumptions regarding the tail fractile sequence, memory and heterogeneity, choosing the sample fractile by non-parametrically minimizing the mean-squared-error leads to a consistent and asymptotically normal estimator. A broad simulation study demonstrates the merits of the resulting minimum MSE estimator for autoregressive and GARCH data. We analyze the distribution of a standardiz ed Hill-estimator in order to asses the accuracy of the kernel e stimator of the asymptotic variance, and the distribution of the minimum MSE estimator. Finally, we apply the estimators to a small study of the tail shape of equity markets returns.

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Bibliographic Info

Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0604.

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Length: 28 pages
Date of creation: May 2006
Date of revision:
Handle: RePEc:fiu:wpaper:0604

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Keywords: Hill estimator; regular variation; extremal near epoch dependence; kernel estimator; mean-square-error.;

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  1. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 99(1), pages 95-115, May.
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