Abstract
In many areas of application, like for instancestatistical quality control, insurance andfinance, a typical requirement is to estimate ahigh quantile, i.e., the Value at Risk at a level p, high enough, so that the chance of an exceedance of that value is equal top, small. In this paper we provide an empirical data analysis of logreturns associated to a set of financial data, through the use of reduced-bias tail index and associated high quantile estimators. These tail index estimators depend on two second order parameters, and in order to achieve a reduction in bias without any inflation of the asymptotic variance, the second order parameters in the bias are both estimated at a level of a higher order than the one used for the estimation of the tail index. A percentile method for quantile estimation and a heuristic adaptive choice of the threshold for reduced-bias estimators are considered, and their finite sample properties are studied via small-scale Monte Carlo simulations.
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Gomes, M.I., Pestana, D., Rodrigues, L., Viseu, C. (2008). Tail Behaviour An Empirical Study. In: Advances in Mathematical and Statistical Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4626-4_14
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DOI: https://doi.org/10.1007/978-0-8176-4626-4_14
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