Kernel Methods for Small Sample and Asymptotic Tail Inference for Dependent, Heterogeneous Data
AbstractThis 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 InfoPaper provided by Florida International University, Department of Economics in its series Working Papers with number 0604.
Length: 28 pages
Date of creation: May 2006
Date of revision:
Hill estimator; regular variation; extremal near epoch dependence; kernel estimator; mean-square-error.;
Find related papers by JEL classification:
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other
- C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-06-03 (All new papers)
- NEP-ECM-2006-06-03 (Econometrics)
- NEP-ETS-2006-06-03 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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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