Tail and Quantile Estimation for Strongly Mixing Stationary Sequences

Abstract

Abstract : This paper primarily concerns the estimation of tail parameters for the marginal distribution F of the terms of a strongly mixing stationary sequence when 1-F(t) decreases exponentially, or is regularly varying as t infinity. The asymptotic properties of the Hill estimator for the exponential parameter or regular variation index are developed within this framework. Estimation procedures are investigated for tail probabilities and tail quantiles, both for the individual terms of the process and for their maxima over groups of consecutive terms. The latter case requires estimation of the so called extremal index, and substantially involves the local dependence structure of the sequence.

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