pwtc {biwavelet}

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
)

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.

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")