Causality in extremes of time series

Consider two stationary time series with heavy-tailed marginal distributions. We aim 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. This paper aims to detect the causal relations in extremes between time series. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between extremes of the 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 asymptotic properties and show how it performs on some simulations. Finally, we show how this method works on space-weather and hydro-meteorological data sets.