Copulas and time series with long-ranged dependencies.

We review ideas on temporal dependencies 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 nonlinear time dependencies and related concepts-like aftershocks, Omori law, recurrences, and 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 monoscale.

Weighted Kolmogorov-Smirnov test: accounting for the tails.

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximate limit solutions found originally in unrelated fields, first in [L. Turban, J. Phys. A 25, 127 (1992)] and later in [P. L. Krapivsky and S. Redner, Am. J. Phys. 64, 546 (1996)].