We consider the nonparametric
estimation of extremal index of stochastic processes with possibly heavy-tailed noise. The extremal index measures the local dependence of extremes of a stationary process and plays a key role in extreme value analysis. Clusters of exceedances of the process over a sufficiently high threshold correspond to outliers those can lead to hazardous events. The reciprocal of the extremal index approximates the mean cluster size. There are several methods like well-known nonparametric blocks, runs and intervals estimators of the extremal index which all require the selection of an appropriate threshold $u$. We propose the discrepancy method based on the von Mises-Smirnov statistic $\omega^2$ as a data-dependent method to estimate $u$. The latter method was applied before as a data-driven smoothing tool for nonparametric estimators of probability density functions as an alternative to cross-validation. In case, the marginal distribution of the process is heavy-tailed it is proposed to calculate the $\omega^2$-statistic by some number of largest order statistics of the sample. The accuracy of the proposed method is studied by simulation.
