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

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 near-epoch-dependent on a mixing process; and obtain a power of one for extremal dependent processes under general conditions. We restrict the NED property to hold only in the extreme support of the distribution, and characterize a broad array of linear and GARCH processes with geometric or hypoberbolic memory that are extremal NED. We apply one-tailed, two-tailed, and difference in tails tests to stock market and exchange rate returns data, and find low levels of significant, persistent, symmetric extremal dependence in the Yen and British Pound, and except for the Shanghai Stock Exchange we find no evidence of extremal dependence in any absolute returns series. A limited study of bivariate volatility spillover in exchange rates reveals extremes in the daily returns of the Yen symmetrically spillover briefly into the Euro after a four day delay, and positive extreme returns in the Euro immediately, and persistently, spillover into the Yen. //