Description: Surrogates Early Warning Signals


surrogates_ews is used to estimate distributions of trends in statistical moments from different surrogate timeseries generated after fitting an ARMA(p,q) model on the data. The trends are estimated by the nonparametric Kendall tau correlation coefficient and can be compared to the trends estimated in the original timeseries to produce probabilities of false positives.


    indicator = c("ar1", "sd", "acf1", "sk", "kurt", "cv", "returnrate", "densratio"),
    winsize = 50,
    detrending = c("no", "gaussian", "linear", "first-diff"),
    bandwidth = NULL, boots = 100, logtransform = FALSE,
    interpolate = FALSE)



a numeric vector of the observed univariate timeseries values or a numeric matrix where the first column represents the time index and the second the observed timeseries values. Use vectors/matrices with headings.


is the statistic (leading indicator) selected for which the surrogate timeseries are produced. Currently, the indicators supported are: ar1 autoregressive coefficient of a first order AR model, sd standard deviation, acf1 autocorrelation at first lag, sk skewness, kurt kurtosis, cv coeffcient of variation, returnrate, and densratio density ratio of the power spectrum at low frequencies over high frequencies.


is the size of the rolling window expressed as percentage of the timeseries length (must be numeric between 0 and 100). Default valuise 50%.


the timeseries can be detrended/filtered prior to analysis. There are three options: gaussian filtering, linear detrending and first-differencing. Default is no detrending.


is the bandwidth used for the Gaussian kernel when gaussian filtering is selected. It is expressed as percentage of the timeseries length (must be numeric between 0 and 100). Alternatively it can be given by the bandwidth selector bw.nrd0 (Default).


the number of surrogate data. Default is 100.


logical. If TRUE data are logtransformed prior to analysis as log(X+1). Default is FALSE.


logical. If TRUE linear interpolation is applied to produce a timeseries of equal length as the original. Default is FALSE (assumes there are no gaps in the timeseries).


see ref below


surrogates_ews returns a matrix that contains:

Kendall tau estimate original

the trends of the original timeseries.

Kendall tau p-value original

the p-values of the trends of the original timeseries.

Kendall tau estimate surrogates

the trends of the surrogate timeseries.

Kendall tau p-value surrogates

the associated p-values of the trends of the surrogate timeseries.

significance p

the p-value for the original Kendall tau rank correlation estimate compared to the surrogates.

In addition, surrogates_ews returns a plot with the distribution of the surrogate Kendall tau estimates and the Kendall tau estimate of the original series. Vertical lines indicate the 5% and 95% significance levels.


Vasilis Dakos


Dakos, V., et al (2008). "Slowing down as an early warning signal for abrupt climate change." Proceedings of the National Academy of Sciences 105(38): 14308-14312

Dakos, V., et al (2012)."Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data." PLoS ONE 7(7): e41010. doi:10.1371/journal.pone.0041010

See Also

generic_ews; ddjnonparam_ews; bdstest_ews; sensitivity_ews; surrogates_ews; ch_ews; movpotential_ews; livpotential_ews

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