Tail estimation and conditional modeling of heteroscedastic time series

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There is currently a surge of interests in the correct modeling of the returns on financial assets, techniques for generations good forecasts and reliable methods for assessing the probability of extrem events, most notably the determination of down-side risk. To this end, we develop tail index estimators specifically designed for data generated from a stable law an demonstrate the cosequences of their use - most notably the overturning of some common findings the literature on the tail-thickness of asset returns data.