In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by B. Hill (1975) for possibly heavy- tailed, heterogenous, dependent processes. We prove the Hill estimator is weakly consistent for processes with extremes that form mixingale sequences, and...

We develop asymptotically chi-squared tests of tail specific extremal serial dependence for possibly heavy-tailed time series, including infinite variance and infinite mean processes. Our test statistics have a chi-squared limit distribution under the null of "extremal white-noise" for processes...