pwtc: Compute partial wavelet coherence

In biwavelet: Conduct univariate and bivariate wavelet analyses

Description

Compute partial wavelet coherence between y and x1 by partialling out the effect of x2

Usage

pwtc (y, x1, x2, 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, nrands = 300, quiet = FALSE)

Arguments

y	time series y in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
x1	time series x1 in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
x2	time series x2 whose effects should be partialled out 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.
nrands	number of Monte Carlo randomizations. Default is 300.
quiet	Do not display progress bar. Default is FALSE

Value

Return a biwavelet object containing:

coi	matrix containg cone of influence
wave	matrix containing the cross-wavelet transform of y and x1
rsq	matrix of partial wavelet coherence between y and x1 (with x2 partialled out)
phase	matrix of phases between y and x1
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
y.sigma	standard deviation of y
x1.sigma	standard deviation of x1
mother	mother wavelet used
type	type of biwavelet object created (pwtc)
signif	matrix containg sig.level percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Note

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 dual-core Xeon processor.

Author(s)

Tarik C. Gouhier ([e-mail])

Code based on WTC MATLAB package written by Aslak Grinsted.

References

Aguiar-Conraria, L., and M. J. Soares. 2013. The Continuous Wavelet Transform: moving beyond uni- and bivariate analysis. Journal of Economic Surveys In press.

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.

Ng, E. K. W., and J. C. L. Chan. 2012. Geophysical applications of partial wavelet coherence and multiple wavelet coherence. Journal of Atmospheric and Oceanic Technology 29:1845-1853.

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.

Examples

y=cbind(1:100, rnorm(100))
x1=cbind(1:100, rnorm(100))
x2=cbind(1:100, rnorm(100))
## Partial wavelet coherence of y and x1
pwtc.yx1=pwtc(y, x1, x2, nrands=0)
## Partial wavelet coherence of y and x2
pwtc.yx2=pwtc(y, x2, x1, nrands=0)
## Plot partial wavelet coherence and phase difference (arrows)
## Make room to the right for the color bar
par(mfrow=c(2,1), oma=c(4, 0, 0, 1), mar=c(1, 4, 4, 5), mgp = c(1.5, 0.5, 0))
plot(pwtc.yx1, xlab="", plot.cb=TRUE, main="Partial wavelet coherence of y and x1 | x2")
plot(pwtc.yx2, plot.cb=TRUE, main="Partial wavelet coherence of y and x2 | x1")

Example output

biwavelet 0.20.11 loaded.

biwavelet documentation built on May 2, 2019, 5:10 p.m.