Which Extreme Values Are Really Extreme?

Jesus Gonzalo

Journal of Financial Econometrics, 2004, vol. 2, issue 3, 349-369

Abstract: We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets. Copyright 2004, Oxford University Press.

Date: 2004
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Working Paper: Which Extreme Values are Really Extremes? (2004)
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