A package with tools to compute early warning signals (EWS) from time-series data

autocorrelation, bifurcation, bootstrapping, complex-systems, critical-transitions, early-warning-indicators, early-warning-signals, forecasting, power-spectrum, resilience-indicators, time-series, tipping-point
pip install ewstools==0.0.10


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Python package for computing, analysing and visualising early warning signals (EWS) in time series data. Includes a novel approach to characterise bifurcations using Spectral EWS.



Many natural and artificial systems have the capacity to undergo a sudden change in their dynamics. In the mathematical realm of dynamical systems, these changes corresopond to bifurcations, and theory therein suggests that certain signals, observable in time series data, should precede these bifurcations (Scheffer et al. 2009). Two commonly used metrics include variance and autocorrelation, though there exist many others (see e.g. Clements & Ozgul 2018). Our objective with this package is to provide a user-friendly toolbox in Python to compute early warning signals from time series data. This complements another early warning signal toolbox written in R (Dakos et al. 2012), and provides novel tools to extract information on the bifurcation from the power spectrum - results to be published soon.

Functionality of ewstools includes

  • Detrending using either

    • Gaussian smoothing
    • A Lowess filter
  • Computation of the following statistical properties over a rolling window:

    • Variance and its derivatives (standard deviation, coefficient of variation)
    • Autocorrelation (at specified lag times)
    • Higher-order moments (skewness, kurtosis)
    • Power spectrum (including maximum frequency, coherence factor and AIC weights csp. to canonical power spectrum forms)
  • Block-bootstrapping time-series to obtain confidence bounds on EWS estimates

  • Visualisation of EWS with plots of time-series and power spectra.

Repo Contents

  • demos: interactive demos in Jupyter notebooks to illustrate use of package
  • docs: version-controlled package documentation provided in ReadTheDocs
  • ewstools: package code
  • nat_comms: supporting code for paper submission to Nature Communications
  • tests: testing of package functions using pytest

System Requirements

Hardware Requirements

ewstools can run on a standard computer with enough RAM to support the operations defined by a user. The software has been tested on a computer with the following specs

RAM: 8G, CPU: 2.7 GHz

though the software should run as expected on computers with lower RAM. The runtimes outlined below were generated on the computer with these specs.

Software Requirements

ewstools requires Python 3.7 or higher and has the following package dependencies:


The Python package should be compatible with Windows, Mac, and Linux operating systems. The demonstrations require Jupyter notebook, which can be installed

Installation Guide

Friendly instructions for downloading Python 3 on Linux, Mac OS and Windows are available here.

Then, the package ewstools may be installed using pip, by entering the following into Terminal (Mac/Linux) or Command Prompt (Windows)

pip install ewstools

which includes all package dependencies. Installation of the package should take less than one minute on a standard computer. To interact with the demos, Jupyter notebook is required, which can be installed using

pip install jupyterlab

and takes no longer than a minute to download.


For interacitve demonstrations on using ewstools, please refer to these iPython notebooks.


Full documentation is available on ReadTheDocs.


If you are interested in being a contributer, or run into trouble with the package, please post on the issue tracker.