sensitivity_ews {earlywarnings}

Sensitivity Early Warning Signals

Description

sensitivity_ews is used to estimate trends in statistical moments for different sizes of rolling windows along a timeseries and the trends are estimated by the nonparametric Kendall tau correlation coefficient.

Usage

sensitivity_ews(
  timeseries,
  indicator = c("ar1", "sd", "acf1", "sk", "kurt", "cv", "returnrate", "densratio"),
  winsizerange = c(25, 75),
  incrwinsize = 25,
  detrending = c("no", "gaussian", "loess", "linear", "first-diff"),
  bandwidthrange = c(5, 100),
  spanrange = c(5, 100),
  degree = NULL,
  incrbandwidth = 20,
  incrspanrange = 10,
  logtransform = FALSE,
  interpolate = FALSE
)

Arguments

timeseries

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.

indicator

is the statistic (leading indicator) selected for which the sensitivity analysis is perfomed. 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.

winsizerange

is the range of the rolling window sizes expressed as percentage of the timeseries length (must be numeric between 0 and 100). Default is 25% - 75%.

incrwinsize

increments the rolling window size (must be numeric between 0 and 100). Default is 25.

detrending

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

bandwidthrange

is the range of 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). Default is 5% - 100%.

spanrange

parameter that controls the degree of smoothing (numeric between 0 and 100). Default is 5% - 100%.

degree

the degree of polynomial to be used for when loess fitting is applied, normally 1 or 2 (Default).

incrbandwidth

is the size to increment the bandwidth used for the Gaussian kernel when gaussian filtering is applied. It is expressed as percentage of the timeseries length (must be numeric between 0 and 100). Default is 20.

incrspanrange

Span range

logtransform

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

interpolate

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).

Details

In addition, sensitivity_ews returns a plot with the Kendall tau estimates and their p-values for the range of rolling window sizes used, together with a histogram of the distributions of the statistic and its significance. When gaussian filtering is chosen, a contour plot is produced for the Kendall tau estimates and their p-values for the range of both rolling window sizes and bandwidth used. A reverse triangle indicates the combination of the two parameters for which the Kendall tau was the highest

Value

sensitivity_ews returns a matrix that contains the Kendall tau rank correlation estimates for the rolling window sizes (rows) and bandwidths (columns), if gaussian filtering is selected.

Author(s)

Vasilis Dakos [e-mail]

References

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

Examples

data(foldbif)
output=sensitivity_ews(foldbif,indicator='sd',detrending='gaussian',
incrwinsize=25,incrbandwidth=20)