This paper conside rs 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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Paper provided by Florida International University, Department of Economics in its series Working Papers with number
0604.
Find related papers by JEL classification: C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
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