Nonlinear time series analysis of palaeoclimate proxy records

Abstract

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability.In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These includeapproaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling.Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5~million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series.We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate.Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.

Recurrence flow measure of nonlinear dependence

“…An RP is based on a binary recurrence matrix in which recurrences are marked by value one, giving rise to intriguing and well-interpretable structures in the RP. Various quantification measures can be applied to a recurrence matrix and prove powerful in classifying differing systems [23][24][25][26], identifying dynamical regime transitions [27,28], and detecting non-linear correlations as well as synchronization [6,29,30]. Recurrence quantification analysis (RQA) based on diagonal lines in the RP not only allows identification of periodic behavior [18,31], but also helps to identify unstable periodic orbits in high-dimensional chaotic systems [32].…”

Recurrence flow measure of nonlinear dependence

“…An RP is based on a binary recurrence matrix in which recurrences are marked by value one, giving rise to intriguing and wellinterpretable structures in the RP. Various quantification measures can be applied to a recurrence matrix and prove powerful in classifying differing systems [23][24][25][26], identifying dynamical regime transitions [27,28], and detecting non-linear correlations as well as synchronization [6,29,30]. Recurrence quantification analysis (RQA) based on diagonal lines in the RP not only allows identification of periodic behaviour [18,31], but also helps to identify unstable periodic orbits in high-dimensional chaotic systems [32].…”

Analysis of Precious Metal Price Movements Using Long Memory Model and Fuzzy Time Series Markov Chain

“…According to Wei (2019), the data has a repeating pattern in which the period in the past tends to reoccur in the present or future. The time series model analysis is meant to determine a pattern or regularity for modeling and identifying the component factors affecting the value in the time series (Marwan et al, 2021). Classic time series models include autoregressive integrated moving averages (ARIMA), time series regression, and exponential smoothing.…”