xwt: Compute cross-wavelet
In biwavelet: Conduct univariate and bivariate wavelet analyses

Description Usage Arguments Value Author(s) References Examples

Compute cross-wavelet

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xwt (d1, d2, pad = TRUE, dj = 1/12, s0 = 2 * dt, J1 = NULL, 
     max.scale = NULL, mother = c("morlet", "paul", "dog"), 
     param = -1, lag1 = NULL, sig.level = 0.95, sig.test = 0)

`d1`	time series 1 in matrix format (`n` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`d2`	time series 2 in matrix format (`n` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`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 2*`dt`
`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 `morlet`, `dog`, or `paul`. Default is `morlet`. Significance testing is only available for `morlet` wavelet.
`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 0.95.
`sig.test`	type of significance test. If set to 0, use a regular χ^2 test. If set to 1, then perform a time-average test. If set to 2, then do a scale-average test.

Returns a biwavelet object containing:

`coi`	matrix containg cone of influence
`wave`	matrix containing the cross-wavelet transform
`wave.corr`	matrix containing the bias-corrected cross-wavelet transform using the method described by `Veleda et al. (2012)`
`power`	matrix of power
`power.corr`	matrix of bias-corrected cross-wavelet power using the method described by `Veleda et al. (2012)`
`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 `biwavelet` object created (`xwt`)
`signif`	matrix containg significance levels

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 156:287-304.

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 11:561-566.

Torrence, C., and G. P. Compo. 1998. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:61-78.

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 124:1985-2004.

Veleda, D., R. Montagne, and M. Araujo. 2012. Cross-Wavelet Bias Corrected by Normalizing Scales. Journal of Atmospheric and Oceanic Technology 29:1401-1408.

t1=cbind(1:100, rnorm(100))
t2=cbind(1:100, rnorm(100))
## Cross-wavelet
xwt.t1t2=xwt(t1, t2)
## Plot cross-wavelet and phase difference (arrows)
plot(xwt.t1t2, plot.cb=TRUE, plot.phase=TRUE)
## Real data
data(enviro.data)
## Cross-wavelet of MEI and NPGO
xwt.mei.npgo=xwt(subset(enviro.data, select=c("date", "mei")), 
        subset(enviro.data, select=c("date", "npgo")))
## 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(xwt.mei.npgo, plot.cb=TRUE, plot.phase=TRUE)