We review ideas on temporal dependences and recurrences in discrete time
series from several areas of natural and social sciences. We revisit existing
studies and redefine the relevant observables in the language of copulas (joint
laws of the ranks). We propose that copulas provide an appropriate mathematical
framework to study non-linear time dependences and related concepts - like
aftershocks, Omori law, recurrences, waiting times. We also critically argue
using this global approach that previous phenomenological attempts involving
only a long-ranged autocorrelation function lacked complexity in that they were
essentially mono-scale.Comment: 11 pages, 8 figure