A model-free characterization of recurrences in stationary time series

TL;DR

This paper advocates for using copulas as a model-free approach to analyze non-linear dependencies and recurrences in stationary time series, revealing limitations of traditional methods and impacting applications like earthquake forecasting and financial risk management.

Contribution

It introduces copulas as a framework for studying non-linear dependencies in recurrences, challenging the universality of previous models and emphasizing system-specific analysis.

Findings

Copulas effectively capture non-linear dependencies in recurrence times.

Traditional autocorrelation-based methods overlook multi-scaling properties.

Recurrence interval modeling requires system-specific approaches.

Abstract

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.