# Critical speeding up as an early warning signal of regime switching

## TL;DR

This paper introduces 'critical speeding up,' a phenomenon where decreasing variance and autocorrelation signal an imminent regime shift due to basin compression, contrasting with traditional critical slowing down indicators.

## Contribution

It identifies and demonstrates a new warning sign, critical speeding up, in systems undergoing regime change, expanding early warning signals beyond critical slowing down.

## Key findings

- Critical speeding up occurs when basin of attraction compresses.
- Variance and autocorrelation decrease before regime shifts.
- Both rising and falling statistical signals can indicate imminent change.

## Abstract

The use of critical slowing down as an early warning indicator for regime switching in observations from stochastic environments and noisy dynamical models has been widely studied and implemented in recent years. Some systems, however, have been shown to avoid critical slowing down prior to a transition between equilibria, e.g. (Ditlevsen and Johnsen, 2010). Possible explanations include non-smooth potential driving the dynamic (Hastings and Wysham, 2010) or large perturbations driving the system out of the initial basin of attraction. In this paper we discuss a phenomenon analogous to critical slowing down, where a slow parameter change leads to a high likelihood of a regime shift and creates signature warning signs in the statistics of the process's sample paths. In short, if a basin of attraction is compressed under a parameter change then the potential well steepens, leading to a drop in the time series' variance and autocorrelation; precisely the opposite warning signs exhibited by critical slowing down. This effect, which we call `critical speeding up,' is demonstrated using a simple ecological model exhibiting an Allee effect. The fact that both dropping and rising variance / autocorrelation can indicate imminent state change should underline the need for reliable modeling of any empirical system where one desires to forecast regime change.