Description Usage Arguments Value Author(s) References See Also
This function provides Morlet wavelet transformation results of the given time series,
performed within the lowerorder function WaveletTransform
,
subject to criteria concerning the time and frequency resolution, and an (optional) lower and/or upper Fourier period.
It performs a simulation algorithm to test against a specified alternative hypothesis, which can be chosen from a variety of options,
and provides pvalues. The selected model will be fitted to the data and simulated according to estimated parameters
in order to provide surrogate time series.
This function is called by function analyze.wavelet
.
The name and parts of the layout were inspired by a similar function developed by Huidong Tian and Bernard Cazelles
(archived R package WaveletCo
).
The major part of the code for the computation of the cone of influence, and the code for Fourierrandomized surrogate time series
has been adopted from Huidong Tian.
1 2 3 4 
x 
the time series to be analyzed 
start 
starting point in time (for the computation of the cone of influence). Default: 
dt 
time resolution, i.e. sampling resolution in the time domain, Default: 
dj 
frequency resolution, i.e. sampling resolution in the frequency domain, Default: 
lowerPeriod 
lower Fourier period (measured in time units determined by Default: 
upperPeriod 
upper Fourier period (measured in time units determined by Default: 
make.pval 
Compute pvalues? Logical. Default: 
method 
the method of generating surrogate time series; select from:
Default:  
params 
a list of assignments between methods (AR, and ARIMA) and lists of parameter values
applying to surrogates. Default: Default includes two lists named

n.sim 
number of simulations. Default: 
save.sim 
Should simulations be saved on the output list? Logical. Default: 
A list with the following elements:
Wave 
complex wavelet transform of the series 
Phase 
phases 
Ampl 
amplitudes 
Power 
wavelet power in the time/frequency domain 
Power.avg 
vector of average wavelet power in the frequency domain (averages over time) 
Power.pval 
pvalues of wavelet power 
Power.avg.pval 
vector of pvalues of average wavelet power 
Period 
the Fourier periods
(measured in time units determined by 
Scale 
the scales (the Fourier periods divided by the Fourier factor) 
coi.1, coi.2 
borders of the region where the wavelet transforms are not influenced by edge effects (cone of influence).
The coordinates of the borders are expressed in terms of internal axes 
nc 
number of columns = number of observations = number of observation epochs; "epoch" meaning point in time 
nr 
number of rows = number of scales (Fourier periods) 
axis.1 
tick levels corresponding to the time steps used for (cross)wavelet transformation: 
axis.2 
tick levels corresponding to the log of Fourier periods: 
series.sim 
a data frame of the series simulated as surrogates for the (detrended) time series
(if both 
Angi Roesch and Harald Schmidbauer; credits are also due to Huidong Tian, and Bernard Cazelles
AguiarConraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.
Carmona R., Hwang W.L., and Torresani B., 1998. Practical Time Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S. Academic Press, San Diego.
Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008. Wavelet analysis of ecological time series. Oecologia 156, 287–304.
Liu Y., Liang X.S., and Weisberg R.H., 2007. Rectification of the Bias in the Wavelet Power Spectrum. Journal of Atmospheric and Oceanic Technology 24, 2093–2102.
Tian, H., and Cazelles, B., 2012. WaveletCo
.
Available at https://cran.rproject.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.
Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61–78.
WaveletTransform
, analyze.wavelet
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