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We review ideas on temporal dependences and recurrences in discrete timeseries from several areas of natural and social sciences. We revisit existingstudies and redefine the relevant observables in the language of copulas (jointlaws of the ranks). We propose that copulas provide an appropriate mathematicalframework to study non-linear time dependences and related concepts - likeaftershocks, Omori law, recurrences, waiting times. We also critically argueusing this global approach that previous phenomenological attempts involvingonly a long-ranged autocorrelation function lacked complexity in that they wereessentially mono-scale.

Copulas and time series with long-ranged dependences