Indicator Description Reference
SD (Standard Deviation) Increasing variance/standard deviation is observed approaching a transition, driven by Critical Slowing Down (CSD). Carpenter and Brock 2006)
CV (Coefficient of Variation) Equivalent to SD as is simply SD at time t divided by the mean SD of the time series. Carpenter and Brock 2006)
AR1 (Autocorrelation at lag1) Autocorrelation (similarity between successive observations) increases approaching a transition, due to CSD. The value of this indicator can be estimated as either the autocorrelation coefficient estimated from a first order autoregressive model or the estimated autocorrelation function at lag1. Held and Kleinen 2004
Skewness At a transition, the distribution of values in the time series can become asymmetric. This is skewness and can increase/decrease depending on the size of the alternative state. Guttal and Jayaprakash 2008
Kurtosis Kurtosis represents the system reaching more extreme values in the presence of a transition. Due to the increased presence of rare values in the time series, the tails of the observation distribution widen. Biggs et al. 2009
Return rate The inverse of the first-order term of a fitted autoregressive AR(1) model. Return rate is the primary quantity impacted by CSD – return rate decreases as a tipping point is approached. (Carpenter et al. 2011)
Density ratio Spectral reddening (high variance at low frequencies) occurs near transition. The density ratio quantifies the degree of reddening as the ratio of the spectral density at low frequency to the spectral density at high frequency. (Kleinen et al. 2003)