The paper describes the details of how modified linear models with time-varying parameters can be used to extract an indicator of instability for a time series that may be drifting towards a regime shift. The paper is available online in Ecosphere and elaborates on time-varying AR(p) and threshold AR(p) models that are presented here. The code to execute all this is currently in Matlab, aiming to convert it into a routine in the R environment.
This fascinating paper by Dai et al demonstrates in a comprehensive way how a simple lab experiment confirms theoretical expectations over critical transitions and early-warning signals. The authors used a yeast population to show how it may shift to extinction at increasing dilution rates. At the same time they were able to demonstrate bistability by identifying the border of the basin of attraction to the extinction state, to measure generic indicators prior to extinction, and measure directly slowing down by perturbation experiments. In short, apply all theory and techniques in the same experiment at once!
Our paper that launched the idea of the Early Warning Signals Toolbox has appeared in PloS One. It is a pure methodological paper that summarizes in a protocol most of the methods being presented for estimating early-warnings in timeseries. In a short time it will be matched with a similar paper on methods using spatial data. Most of the content of both papers will be found in this webpage in a simpler format. Stay in tune!
Welcome to the Early Warning Signals Toolbox!
Here, you can find methods for estimating statistical changes in time series and spatial datasets that can be used for the timely identification of critical transitions in complex systems ranging from ecosystems and climate to neural cells and financial markets.
The toolbox is currently under constant updating!