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.
Chaire de finance quantitative, École Centrale Paris, 92 295 Châtenay-Malabry, France.
Rémy
R
Chicheportiche
Chaire de finance quantitative, École Centrale Paris, 92 295 Châtenay-Malabry, France.
Anirban
A
Chakraborti
D000465:Algorithms; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors