pwtc: Compute partial wavelet coherence

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 = "morlet",
  param = -1,
  lag1 = NULL,
  sig.level = 0.95,
  sig.test = 0,
  nrands = 300,
  quiet = 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

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.
dj: Spacing between successive scales.
s0: Smallest scale of the wavelet.
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. 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.
sig.test: Type of significance test. If set to 0, use a regular \(\chi^2\) 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.
quiet: Do not display progress bar.

Author

Tarik C. Gouhier (tarik.gouhier@gmail.com) 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

Run this code

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")

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