Advances in Recurrence Analysis for Predictive Modeling and Dynamic Classification

Abstract

The recurrence of similar states is a fundamental property of the processes that shape and influence our living and non-living world. There are numerous examples of geological and climatic processes on both short and long time and spatial scales, such as the regular activity of geysers within minutes, the more irregular but still recurrent occurrence of earthquakes (on time scales between weeks and years), the El Niño climate phenomenon occurring every three to five years, the glacial cycles (thousands of years), or the Milanković cycles, which periodically force climate changes up to hundreds of thousands of years. The recurrence of states in such dynamic processes generates typical recurrence patterns that can be used to detect regime changes, to classify the dynamics, or even to predict future changes. I will report on recent achievements in recurrence analysis in recent years, including methodological developments tailored for challenging data in the geosciences, such as irregularly sampled data or extreme event data. The overview includes further important and innovative developments, such as conceptual recurrence plots, ideas for parameter selection, multiscale recurrences, correction schemes, and new perspectives by combining recurrence analysis with machine learning.