Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Strochastic Processes with an Application

We develop a non-parametric test of tail-specific extremal serial dependence for possibly heavy-tailed time series. The test statistic is asymptotically chi-squared under a null of "extremal white noise", as long as extremes of the time series are Near-Epoch-Dependent on the extremes of some mixing process. The theory covers ARFIMA, FIGARCH, bilinear, and Extremal Threshold processes, and a wide range of nonlinear distributed lags. In this setting the test statistic obtains an asymptotic power of one under the alternative. Of separate interest, we deliver a joint distribution limit for an arbitrary vector of tail index estimators under extraordinarily gene ral conditions, complete with a consistent kernel estimator of the covariance matrix. We apply tail specific tests to equity market and exchange rate returns data.