Package 'vectorwavelet' reference manual

Title:	Vector Wavelet Coherence for Multiple Time Series
Description:	New wavelet methodology (vector wavelet coherence) (Oygur, T., Unal, G, 2020 <doi:10.1007/s40435-020-00706-y>) to handle dynamic co-movements of multivariate time series via extending multiple and quadruple wavelet coherence methodologies. This package can be used to perform multiple wavelet coherence, quadruple wavelet coherence, and n-dimensional vector wavelet coherence analyses.
Authors:	Tunc Oygur [aut, cre], Gazanfer Unal [aut], Tarik C. Gouhier [ctb], Aslak Grinsted [ctb], Viliam Simko [ctb]
Maintainer:	Tunc Oygur <[email protected]>
License:	GPL (>=2)
Version:	0.1.0
Built:	2025-02-13 05:44:24 UTC
Source:	https://github.com/toygur/vectorwavelet

Vector wavelet coherence for multiple time series

Description

Description: This package can be used to perform multiple wavelet coherence (mwc), quadruple wavelet coherence (qmwc), and n-dimensional vector wavelet coherence (vwc) analyses.

Author(s)

Tunc Oygur, Gazanfer Unal

Maintainer: Tunc Oygur <[email protected]>

Code based on biwavelet package written by Tarik C. Gouhier, Aslak Grinsted, Viliam Simko.

References

T. Oygur, G. Unal.. Vector wavelet coherence for multiple time series. Int. J. Dynam. Control (2020).

T. Oygur, G. Unal.. The large fluctuations of the stock return and financial crises evidence from Turkey: using wavelet coherency and VARMA modeling to forecast stock return. Fluctuation and Noise Letters, 2017

T.C. Gouhier, A. Grinstead and V. Simko. 2016. biwavelet: Conduct univariate and bivariate wavelet analyses (Version 0.20.15). Available from http://github.com/tgouhier/biwavelet

Ng, Eric KW and Chan, Johnny CL. 2012. Geophysical applications of partial wavelet coherence and multiple wavelet coherence. Journal of Atmospheric and Oceanic Technology 29-12:1845–1853.

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.

AR1NV - Estimate the parameters for an AR(1) model

Description

AR1NV - Estimate the parameters for an AR(1) model

Usage

ar1nv(x)
ar1nv(x)

Arguments

`x`	One dimensional time series vector

Value

Return a list containing:

`g`	estimate of the lag-one autocorrelation.
`a`	estimate of the noise variance.

Author(s)

Tunc Oygur ([email protected])

Code based on a cross wavelet and wavelet coherence toolbox MATLAB package written by Eric Breitenberger

References

SGrinsted, 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.

Compute multiple wavelet coherence

Description

Compute multiple wavelet coherence

Usage

mwc(
  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
)
mwc(
  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 1 in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x1`	time series 2 in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x2`	time series 3 in matrix format (`m` 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 $\chi^2$ 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. Default is 300.
`quiet`	Do not display progress bar. Default is `FALSE`

Value

Return a vectorwavelet object containing:

`coi`	matrix containg cone of influence
`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
`mother`	mother wavelet used
`type`	type of `vectorwavelet` object created (`mwc`)
`signif`	matrix containg `sig.level` percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Author(s)

Tunc Oygur ([email protected])

Code based on MWC MATLAB package written by Eric K. W. Ng and Johnny C. L. Chan.

References

T. Oygur, G. Unal.. Vector wavelet coherence for multiple time series. Int. J. Dynam. Control (2020).

T. Oygur, G. Unal. 2017. The large fluctuations of the stock return and financial crises evidence from Turkey: using wavelet coherency and VARMA modeling to forecast stock return. Fluctuation and Noise Letters

Ng, Eric KW and Chan, Johnny CL. 2012. Geophysical applications of partial wavelet coherence and multiple wavelet coherence. Journal of Atmospheric and Oceanic Technology 29-12:1845–1853.

Examples

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/8)
x2 <- sin(t*2*pi/32)

y <- cbind(t,y)
x1 <- cbind(t,x1)
x2 <- cbind(t,x2)

## Multiple wavelet coherence
result <- mwc(y, x1, x2, nrands = 10)

result <- mwc(y, x1, x2)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot multiple wavelet coherence")

par(old.par)

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/8)
x2 <- sin(t*2*pi/32)

y <- cbind(t,y)
x1 <- cbind(t,x1)
x2 <- cbind(t,x2)

## Multiple wavelet coherence
result <- mwc(y, x1, x2, nrands = 10)

result <- mwc(y, x1, x2)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot multiple wavelet coherence")

par(old.par)

Check the format of multivariate time series

Description

Check the format of multivariate time series

Usage

n.check.data(y, x = NULL)
n.check.data(y, x = NULL)

Arguments

`y`	time series y in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x`	multivariate time series x in matrix format (`m` rows x (1 + (n-1)) columns). The first column should contain the time steps and the other columns should contain the values.

Value

Returns a named list containing:

`t`	time steps
`dt`	size of a time step
`n.obs`	number of observations

Author(s)

Tunc Oygur ([email protected])

Code based on biwavelet package written by Tarik C. Gouhier.

Examples

#Example 1:
t1 <- cbind(1:100, rnorm(100))
n.check.data(y = t1)

#Example 2:
t1 <- cbind(1:100, rnorm(100))
t2 <- cbind(1:100, rnorm(100), rnorm(100), rnorm(100))
n.check.data(y = t1, x = t2)


#Example 1:
t1 <- cbind(1:100, rnorm(100))
n.check.data(y = t1)

#Example 2:
t1 <- cbind(1:100, rnorm(100))
t2 <- cbind(1:100, rnorm(100), rnorm(100), rnorm(100))
n.check.data(y = t1, x = t2)

Helper function

Description

Helper function

Usage

n.check.datum(x)
n.check.datum(x)

Arguments

x

matrix

Value

list(t, dt, n.obs)

Note

This function is not exported

Plot `vectorwavelet` objects

Description

Plot vectorwavelet objects which are multiple wavelet coherence, quadruple wavelet coherence and n-dimensional vector wavelet coherence.

Usage

## S3 method for class 'vectorwavelet'
plot(
  x,
  ncol = 1024,
  fill.cols = NULL,
  xlab = "Time",
  ylab = "Period",
  tol = 1,
  plot.cb = FALSE,
  plot.coi = TRUE,
  lwd.coi = 1,
  col.coi = "white",
  lty.coi = 1,
  alpha.coi = 0.5,
  plot.sig = TRUE,
  lwd.sig = 4,
  col.sig = "black",
  lty.sig = 1,
  bw = FALSE,
  legend.loc = NULL,
  legend.horiz = FALSE,
  arrow.len = min(par()$pin[2]/30, par()$pin[1]/40),
  arrow.lwd = arrow.len * 0.3,
  arrow.cutoff = 0.7,
  arrow.col = "black",
  xlim = NULL,
  ylim = NULL,
  zlim = c(0, 1),
  xaxt = "s",
  yaxt = "s",
  form = "%Y",
  ...
)
## S3 method for class 'vectorwavelet'
plot(
  x,
  ncol = 1024,
  fill.cols = NULL,
  xlab = "Time",
  ylab = "Period",
  tol = 1,
  plot.cb = FALSE,
  plot.coi = TRUE,
  lwd.coi = 1,
  col.coi = "white",
  lty.coi = 1,
  alpha.coi = 0.5,
  plot.sig = TRUE,
  lwd.sig = 4,
  col.sig = "black",
  lty.sig = 1,
  bw = FALSE,
  legend.loc = NULL,
  legend.horiz = FALSE,
  arrow.len = min(par()$pin[2]/30, par()$pin[1]/40),
  arrow.lwd = arrow.len * 0.3,
  arrow.cutoff = 0.7,
  arrow.col = "black",
  xlim = NULL,
  ylim = NULL,
  zlim = c(0, 1),
  xaxt = "s",
  yaxt = "s",
  form = "%Y",
  ...
)

Arguments

`x`	`vectorwavelet` object generated by `mwc`, `qmec`, or `vwc`.
`ncol`	number of colors to use. Default is 1024.
`fill.cols`	Vector of fill colors to be used. Users can specify color vectors using `colorRampPalette` or `brewer.pal` from package `RColorBrewer`. Default is `NULL` and will generate MATLAB's jet color palette.
`xlab`	xlabel of the figure. Default is "Time"
`ylab`	ylabel of the figure. Default is "Period"
`tol`	tolerance level for significance contours. Sigificance contours will be drawn around all regions of the spectrum where `spectrum/percentile >= tol`. Default is `1`. If strict `i^{th}` percentile regions are desired, then `tol` must be set to `1`.
`plot.cb`	plot color bar if TRUE. Default is FALSE.
`plot.coi`	plot cone of influence (COI) as a semi-transparent polygon if TRUE. Default is TRUE. Areas that fall within the polygon can be affected by edge effects.
`lwd.coi`	Line width of COI. Default is 1.
`col.coi`	Color of COI. Default is `white`.
`lty.coi`	Line type of COI. Default is 1 for solide lines.
`alpha.coi`	Transparency of COI. Range is 0 (full transparency) to 1 (no transparency). Default is 0.5.
`plot.sig`	plot contours for significance if TRUE. Default is TRUE.
`lwd.sig`	Line width of significance contours. Default is 4.
`col.sig`	Color of significance contours. Default is `black`.
`lty.sig`	Line type of significance contours. Default is 1.
`bw`	plot in black and white if TRUE. Default is FALSE.
`legend.loc`	legend location coordinates as defined by `image.plot`. Default is `NULL`.
`legend.horiz`	plot a horizontal legend if TRUE. Default is FALSE.
`arrow.len`	size of the arrows. Default is based on plotting region (min(par()$pin[2]/30,par()$pin[1]/40).
`arrow.lwd`	width/thickness of arrows. Default is arrow.len*0.3.
`arrow.cutoff`	cutoff value for plotting phase arrows. Phase arrows will be be plotted in regions where the significance of the zvalues exceeds `arrow.cutoff`. If the object being plotted does not have a significance field, regions whose zvalues exceed the `arrow.cutoff` quantile will be plotted. Default is 0.7.
`arrow.col`	Color of arrows. Default is `black`.
`xlim`	the x limits. The default is `NULL`.
`ylim`	the y limits. The default is `NULL`.
`zlim`	the z limits. The default is `NULL`.
`xaxt`	Add x-axis? The default is `s`; use `n` for none.
`yaxt`	Add y-axis? The default is `s`; use `n` for none.
`form`	format to use to display dates on the x-axis. Default is '%Y' for 4-digit year. See `?Date` for other valid formats.
`...`	other parameters.

Value

No return value, shows the objects plot.

Author(s)

Tunc Oygur ([email protected])

Code based on biwavelet package written by Tarik C. Gouhier.

Compute quadruple wavelet coherence

Description

Compute quadruple wavelet coherence

Usage

qmwc(
  y,
  x1,
  x2,
  x3,
  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
)
qmwc(
  y,
  x1,
  x2,
  x3,
  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 1 in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x1`	time series 2 in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x2`	time series 3 in matrix format (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x3`	time series 4 in matrix format (`m` 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 $\chi^2$ 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. Default is 300.
`quiet`	Do not display progress bar. Default is `FALSE`

Value

Return a vectorwavelet object containing:

`coi`	matrix containg cone of influence
`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
`mother`	mother wavelet used
`type`	type of `vectorwavelet` object created (`qmwc`)
`signif`	matrix containg `sig.level` percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Author(s)

Tunc Oygur ([email protected])

References

T. Oygur, G. Unal.. Vector wavelet coherence for multiple time series. Int. J. Dynam. Control (2020).

Examples

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/16)
x2 <- sin(t*2*pi/32)
x3 <- sin(t*2*pi/64)

y <- cbind(t,y)
x1 <- cbind(t,x1)
x2 <- cbind(t,x2)
x3 <- cbind(t,x3)

## Quadruple wavelet coherence
result <- qmwc(y, x1, x2, x3, nrands = 10)

result <- qmwc(y, x1, x2, x3)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot quadruple wavelet coherence")

par(old.par)

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/16)
x2 <- sin(t*2*pi/32)
x3 <- sin(t*2*pi/64)

y <- cbind(t,y)
x1 <- cbind(t,x1)
x2 <- cbind(t,x2)
x3 <- cbind(t,x3)

## Quadruple wavelet coherence
result <- qmwc(y, x1, x2, x3, nrands = 10)

result <- qmwc(y, x1, x2, x3)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot quadruple wavelet coherence")

par(old.par)

Compute n-dimensional vector wavelet coherence

Description

Compute n-dimensional vector wavelet coherence

Usage

vwc(
  y,
  x,
  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
)
vwc(
  y,
  x,
  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 (`m` rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
`x`	multivariate time series x in matrix format (`m` rows x n columns). The first column should contain the time steps and the other columns 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 $\chi^2$ 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. Default is 300.
`quiet`	Do not display progress bar. Default is `FALSE`

Value

Return a vectorwavelet object containing:

`coi`	matrix containg cone of influence
`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
`mother`	mother wavelet used
`type`	type of `vectorwavelet` object created (`vwc`)
`signif`	matrix containg `sig.level` percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Author(s)

Tunc Oygur ([email protected])

References

T. Oygur, G. Unal.. Vector wavelet coherence for multiple time series. Int. J. Dynam. Control (2020).

Examples

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/8)
x2 <- sin(t*2*pi/16)
x3 <- sin(t*2*pi/32)
x4 <- sin(t*2*pi/64)

y <- cbind(t,y)
x <- cbind(t,x1,x2,x3,x4)

## n-dimensional multiple wavelet coherence
result <- vwc(y, x, nrands = 10)

result <- vwc(y, x)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot n-dimensional vwc (n=5)")

par(old.par)

old.par <- par(no.readonly=TRUE)

t <- (-100:100)

y <- sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64)
x1 <- sin(t*2*pi/8)
x2 <- sin(t*2*pi/16)
x3 <- sin(t*2*pi/32)
x4 <- sin(t*2*pi/64)

y <- cbind(t,y)
x <- cbind(t,x1,x2,x3,x4)

## n-dimensional multiple wavelet coherence
result <- vwc(y, x, nrands = 10)

result <- vwc(y, x)


## Plot wavelet coherence and make room to the right for the color bar
## Note: plot function can be used instead of plot.vectorwavelet
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1,  pin = c(3,3))
plot.vectorwavelet(result, plot.cb = TRUE, main = "Plot n-dimensional vwc (n=5)")

par(old.par)

Package 'vectorwavelet'

Help Index

Vector wavelet coherence for multiple time series

Description

Author(s)

References

AR1NV - Estimate the parameters for an AR(1) model

Description

Usage

Arguments

Value

Author(s)

References

Compute multiple wavelet coherence

Description

Usage

Arguments

Value

Author(s)

References

Examples

Check the format of multivariate time series

Description

Usage

Arguments

Value

Author(s)

Examples

Helper function

Description

Usage

Arguments

Value

Note

Plot vectorwavelet objects

Description

Usage

Arguments

Value

Author(s)

Compute quadruple wavelet coherence

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute n-dimensional vector wavelet coherence

Description

Usage

Arguments

Value

Author(s)

References

Examples

Plot `vectorwavelet` objects