An adaptive optimal estimate of the tail index for MA(l) time series

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second-order regular variation is needed. In this paper we first supplement earlier results on convolution given by Geluk et al. (Stochastic Process. Appl. 69 (1997) 138-159). Secondly, we propose a simple estimator of the tail index for finite moving average time series. We also give a subsampling procedure in order to estimate the optimal sample fraction in the sense of minimal mean squared error.