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. If the powerspectrum is to be plotted as well,
the timeseries lenght should be even number.
winsize
is the size of the rolling window
expressed as percentage of the timeseries length (must be
numeric between 0 and 100). Default is 50%.
bandwidth
is 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). Alternatively it can be given
by the bandwidth selector bw.nrd0
(Default).
detrending
the timeseries can be
detrended/filtered prior to analysis. There are four
options: gaussian filtering, loess fitting,
linear detrending and first-differencing.
Default is no detrending.
span
parameter that controls the degree of
smoothing (numeric between 0 and 100, Default 25). see
more on loessstats
degree
the degree of polynomial to be used for
when loess fitting is applied, normally 1 or 2 (Default).
see more on loessstats
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).
AR_n
logical. If TRUE the best fitted AR(n) model
is fitted to the data. Default is FALSE.
powerspectrum
logical. If TRUE the power spectrum
within each rolling window is plotted. Default is FALSE.
Details
see ref below
Value
generic_ews returns a matrix that contains:
tim
the time index.
ar1
the autoregressive coefficient ar(1) of a
first order AR model fitted on the data within the rolling
window.
sd
the standard deviation of the data
estimated within each rolling window.
sk
the skewness of the data estimated within
each rolling window.
kurt
the kurtosis of the data estimated
within each rolling window.
cv
the coefficient of variation of the data
estimated within each rolling window.
returnrate
the return rate of the data estimated as
1-ar(1) cofficient within each rolling window.
densratio
the density ratio of the power
spectrum of the data estimated as the ratio of low
frequencies over high frequencies within each rolling
window.
acf1
the autocorrelation at first lag of the
data estimated within each rolling window.
In addition, generic_ews returns three plots. The
first plot contains the original data, the
detrending/filtering applied and the residuals (if
selected), and all the moment statistics. For each
statistic trends are estimated by the nonparametric Kendall
tau correlation. The second plot, if asked, quantifies
resilience indicators fitting AR(n) selected by the Akaike
Information Criterion. The third plot, if asked, is the
power spectrum estimated by spec.ar for all
frequencies within each rolling window.
Ives, A. R. (1995). 'Measuring resilience in stochastic
systems.' Ecological Monographs 65: 217-233
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