An Adaptive Optimal Estimate of the Tail Index for Ma(l) Time Series

for MA(l) time series J.L. Geluk Liang Peng y Econometric Institute 1 Report EI-9910-A Abstract 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 rst supplement earlier results on convolution given by Geluk et al. (1997). Secondly we propose a simple estimator of the tail index for nite 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.