  Study of recurrences in earthquakes, climate, financial time-series, etc. is
crucial to better forecast disasters and limit their consequences. However,
almost all the previous phenomenological studies involved only a long-ranged
autocorrelation function, or disregarded the multi-scaling properties induced
by potential higher order dependencies. Consequently, they missed the facts
that non-linear dependences do impact both the statistics and dynamics of
recurrence times, and that scaling arguments for the unconditional distribution
may not be applicable. We argue that copulas is the correct model-free
framework to study non-linear dependencies in time series and related concepts
like recurrences. Fitting and/or simulating the intertemporal distribution of
recurrence intervals is very much system specific, and cannot actually benefit
from universal features, in contrast to the previous claims. This has important
implications in epilepsy prognosis and financial risk management applications.
