Description Usage Arguments Value Author(s) References
This function provides Morlet crosswavelet transformation results of the given two time series,
performed within the lowerorder functions WaveletCoherency
and WaveletTransform
subject to criteria concerning the time and frequency resolution, an (optional) lower and/or upper Fourier period,
and a variety of filtering methods for the coherence computation.
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.coherency
.
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 have been adopted from Huidong Tian.
The implementation of a choice of filtering windows for the computation of
the wavelet coherence was inspired by Luis AguiarConraria and Maria Joana Soares (GWPackage
).
1 2 3 4 5 6 
x 
the time series x to be analyzed 
y 
the time series y to be analyzed (of the same length as x 
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: 
window.type.t 
type of window for smoothing in time direction; select from:
Default:  
window.type.s 
type of window for smoothing in scale (period) direction; select from:
Default:  
window.size.t 
size of the window used for smoothing in time direction, measured in time units
determined by  
window.size.s 
size of the window used for smoothing in scale (period) direction in units of 
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 
Shall simulations be saved on the output list? Logical. 
A list with the following elements:
Wave.xy 
(complexvalued) crosswavelet transform (analogous to Fourier crossfrequency spectrum, and to the covariance in statistics) 
Angle 
phase difference, i.e. phase lead of x over y (= 
sWave.xy 
smoothed (complexvalued) crosswavelet transform 
sAngle 
phase difference, i.e. phase lead of x over y, affected by smoothing 
Power.xy 
crosswavelet power (analogous to Fourier crossfrequency power spectrum) 
Power.xy.avg 
average crosswavelet power in the frequency domain (averages over time) 
Power.xy.pval 
pvalues of crosswavelet power 
Power.xy.avg.pval 
pvalues of average crosswavelet power 
Coherency 
(complexvalued) wavelet coherency of series x over series y in the time/frequency domain, affected by smoothing (analogous to Fourier coherency, and to the coefficient of correlation in statistics) 
Coherence 
wavelet coherence (analogous to Fourier coherence, and to the coefficient of determination in statistics (affected by smoothing) 
Coherence.avg 
average wavelet coherence in the frequency domain (averages across time) 
Coherence.pval 
pvalues of wavelet coherence 
Coherence.avg.pval 
pvalues of average wavelet coherence 
Wave.x, Wave.y 
(complexvalued) wavelet transforms of series x and y 
Phase.x, Phase.y 
phases of series x and y 
Ampl.x, Ampl.y 
amplitudes of series x and y 
Power.x, Power.y 
wavelet power of series x and y 
Power.x.avg, Power.y.avg 
average wavelet power of series x and y, averages across time 
Power.x.pval, Power.y.pval 
pvalues of wavelet power of series x and y 
Power.x.avg.pval, Power.y.avg.pval 
pvalues of average wavelet power of series x and y 
sPower.x, sPower.y 
smoothed wavelet power of series x and y 
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, Bernard Cazelles, Luis AguiarConraria, and Maria Joana Soares.
AguiarConraria L., and Soares M.J., 2011. Business cycle synchronization and the Euro: A wavelet analysis. Journal of Macroeconomics 33 (3), 477–489.
AguiarConraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.
AguiarConraria L., and Soares M.J., 2012. GWPackage
.
Available at https://sites.google.com/site/aguiarconraria/joanasoareswavelets; accessed September 4, 2013.
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 P.C., 1994. Wavelet spectrum analysis and ocean wind waves. In: FoufoulaGeorgiou E., and Kumar P., (eds.), Wavelets in Geophysics, Academic Press, San Diego, 151–166.
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.
Veleda D., Montagne R., and Araujo M., 2012. CrossWavelet Bias Corrected by Normalizing Scales. Journal of Atmospheric and Oceanic Technology 29, 1401–1408.
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