On tail dependence parameters for non-continuous and autocorrelated margins

Tail dependence plays an essential role in the characterization of joint extreme events in multivariate data. However, most standard tail dependence parameters assume continuous margins. This note presents a form of tail dependence suitable for non-continuous and discrete margins. We derive a representation of tail dependence based on the volume of a copula and prove its properties. We utilize a bivariate regular variation to show that our new metric is consistent with the standard tail dependence parameters on continuous margins. We further define tail dependence on autocorrelated margins where the tail dependence parameter examine lagged correlation on the sample.