Compute wavelet coherence
1 2 3 
d1 
time series 1 in matrix format ( 
d2 
time series 2 in matrix format ( 
pad 
pad the values will with zeros to increase the speed of the transform. Default is TRUE. 
dj 
spacing between successive scales. Default is 1/12. 
s0 
smallest scale of the wavelet. Default is 
J1 
number of scales  1. 
max.scale 
maximum scale. Computed automatically if left unspecified. 
mother 
type of mother wavelet function to use. Can be set to

param 
nondimensional parameter specific to the wavelet function. 
lag1 
vector containing the AR(1) coefficient of each time series. 
sig.level 
significance level. Default is 
sig.test 
type of significance test. If set to 0, use a regular χ^2 test. If set to 1, then perform a timeaverage test. If set to 2, then do a scaleaverage test. 
nrands 
number of Monte Carlo randomizations. Default is 300. 
quiet 
Do not display progress bar. Default is 
Return a biwavelet
object containing:
coi 
matrix containg cone of influence 
wave 
matrix containing the crosswavelet transform 
wave.corr 
matrix containing the biascorrected crosswavelet transform
using the method described by 
power 
matrix of power 
power.corr 
matrix of biascorrected crosswavelet power using the method described
by 
rsq 
matrix of wavelet coherence 
phase 
matrix of phases 
period 
vector of periods 
scale 
vector of scales 
dt 
length of a time step 
t 
vector of times 
xaxis 
vector of values used to plot xaxis 
s0 
smallest scale of the wavelet 
dj 
spacing between successive scales 
d1.sigma 
standard deviation of time series 1 
d2.sigma 
standard deviation of time series 2 
mother 
mother wavelet used 
type 
type of 
signif 
matrix containg 
The Monte Carlo randomizations can be extremely slow for large datasets. For instance, 1000 randomizations of a dataset consisting of 1000 samples will take ~30 minutes on a 2.66 GHz dualcore Xeon processor.
Tarik C. Gouhier (tarik.gouhier@gmail.com)
Code based on WTC MATLAB package written by Aslak Grinsted.
Cazelles, B., M. Chavez, D. Berteaux, F. Menard, J. O. Vik, S. Jenouvrier, and N. C. Stenseth. 2008. Wavelet analysis of ecological time series. Oecologia 156:287304.
Grinsted, A., J. C. Moore, and S. Jevrejeva. 2004. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics 11:561566.
Torrence, C., and G. P. Compo. 1998. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:6178.
Torrence, C., and P. J. Webster. 1998. The annual cycle of persistence in the El Nino/Southern Oscillation. Quarterly Journal of the Royal Meteorological Society 124:19852004.
Veleda, D., R. Montagne, and M. Araujo. 2012. CrossWavelet Bias Corrected by Normalizing Scales. Journal of Atmospheric and Oceanic Technology 29:14011408.
1 2 3 4 5 6 7 8 9 10  t1 < cbind(1:100, rnorm(100))
t2 < cbind(1:100, rnorm(100))
## Wavelet coherence
wtc.t1t2 < wtc(t1, t2, nrands = 10)
## Plot wavelet coherence and phase difference (arrows)
## Make room to the right for the color bar
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1)
plot(wtc.t1t2, plot.cb = TRUE, plot.phase = TRUE)

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