Detection of causality in time series using extreme values

Consider two stationary time series with heavy-tailed marginal distributions. We want to detect whether they have a causal relation, that is, if a change in one of them causes a change in the other. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this article, we propose new insight that can help with causal detection in such a non-traditional case. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between different time series. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we mention how our method can help detect a time delay between the two time series. We describe some of its properties, and show how it performs on some simulations. Finally, we show on a space-weather and hydro-meteorological data sets how this method works in practice.