Early-warning indicators in the dynamic regime

TL;DR

This paper investigates the accuracy of early-warning indicators like autocorrelation and variance in detecting tipping points, focusing on errors caused by assumptions of stationarity and linearity in time series analysis.

Contribution

It analyzes the discrepancy between theoretical and observed early-warning indicators near bifurcation points in a saddle-node normal form model.

Findings

Theoretical formulas may overestimate early-warning signals near bifurcations.

Errors are primarily due to non-stationarity and nonlinearity in real systems.

The study quantifies the difference between predicted and actual indicators.

Abstract

Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the fluctuations around an equilibrium observed in time series data by a linear stationary (Ornstein-Uhlenbeck) process. Then for the approach of a bifurcation-type tipping point the formulas for the autocorrelation and variance of an Ornstein-Uhlenbeck process detect the phenomenon `critical slowing down'. The assumption of stationarity and linearity introduces two sources of error in the early-warning indicators. We investigate the difference between the theoretical and observed values for the early-warning indicators for the saddle-node normal form bifurcation with linear drift.