WaveletCoherency: Computation of the cross-wavelet power and wavelet coherence of two time series

Description

Given two time series x and y having the same length and timestamp, this function computes the cross-wavelet power and wavelet coherence applying the Morlet wavelet, subject to criteria concerning: the time and frequency resolution, an (optional) lower and/or upper Fourier period, and filtering method for the coherence computation.

The output is further processed by the higher-order function wc and can be retrieved from analyze.coherency.

The name and layout were inspired by a similar function developed by Huidong Tian and Bernard Cazelles (archived R package WaveletCo). The implementation of a choice of filtering windows for the computation of the wavelet coherence was inspired by Luis Aguiar-Conraria and Maria Joana Soares (GWPackage).

Usage

WaveletCoherency(x, y, dt = 1, dj = 1/20,  lowerPeriod = 2*dt, upperPeriod = floor(length(x)*dt/3),  window.type.t = 1, window.type.s = 1,  window.size.t = 5, window.size.s = 1/4)

Arguments

the time series x to be analyzed

the time series y to be analyzed (of the same length as x

time resolution, i.e. sampling resolution on time domain, 1/dt = number of intervals per time step. Default: 1.

frequency resolution, i.e. sampling resolution on frequency domain, 1/dj = number of suboctaves (voices per octave). Default: 1/20.

lowerPeriod

lower Fourier period (in time units) for wavelet decomposition. Default: 2*dt.

upperPeriod

upper Fourier period (in time units) for wavelet decomposition. Default: (floor of one third of time series length)*dt.

window.type.t

type of window for smoothing in time direction, select from:

	0	("none")	:
no smoothing in time direction		1	("bar")
:	Bartlett		2
("tri")	:	Triangular (Non-Bartlett)
3	("box")	:	Boxcar (Rectangular, Dirichlet)
	4	("han")	:
Hanning		5	("ham")
:	Hamming		0

Default: 1 = "bar".

window.type.s

type of window for smoothing in scale (period) direction, select from:

	0	("none")	:
no smoothing in scale (period) direction		1	("bar")
:	Bartlett		2
("tri")	:	Triangular (Non-Bartlett)
3	("box")	:	Boxcar (Rectangular, Dirichlet)
	4	("han")	:
Hanning		5	("ham")
:	Hamming		0

Default: 1 = "bar".

window.size.t

size of the window used for smoothing in time direction in units of 1/dt. Default: 5, which together with dt=1 defines a window of length 5*(1/dt) = 5. Windows of even-numbered sizes are extended by 1.

window.size.s

size of the window used for smoothing in scale direction in units of 1/dj. Default: 1/4, which together with dj=1/20 defines a window of length (1/4)*(1/dj) = 5. Windows of even-numbered sizes are extended by 1.

Value

Wave.xy: (complex-valued) cross-wavelet transform (analogous to Fourier cross-frequency spectrum, and to the covariance in statistics)
sWave.xy: smoothed (complex-valued) cross-wavelet transform
Power.xy: cross-wavelet power (analogous to Fourier cross-frequency power spectrum)
Coherency: (complex-valued) wavelet coherency of series x over series y in the time/frequency domain, affected by smoothing (analogous to Fourier coherency, and to the coefficient of correlation in statistics)
Coherence: wavelet coherence (analogous to Fourier coherence, and to the coefficient of determination in statistics (affected by smoothing)
Wave.x, Wave.y: (complex-valued) wavelet transforms of series x and y
Phase.x, Phase.y: phases of series x and y
Ampl.x, Ampl.y: amplitudes of series x and y
Power.x, Power.y: wavelet power of series x and y
sPower.x, sPower.y: smoothed wavelet power of series x and y
Period: the Fourier periods (in time units)
Scale: the scales
nc: number of columns/time steps
nr: number of rows/scales

References

Aguiar-Conraria L., and Soares M.J., 2011. Business cycle synchronization and the Euro: A wavelet analysis. Journal of Macroeconomics 33 (3), 477--489.

Aguiar-Conraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.

Aguiar-Conraria L., and Soares M.J., 2012. GWPackage. Available at http://sites.google.com/site/aguiarconraria/joanasoares-wavelets; accessed September 4, 2013.

Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008. Wavelet analysis of ecological time series. Oecologia 156, 287--304.

Liu P.C., 1994. Wavelet spectrum analysis and ocean wind waves. In: Foufoula-Georgiou E., and Kumar P., (eds.), Wavelets in Geophysics, Academic Press, San Diego, 151--166.

Tian, H., and Cazelles, B., 2012. WaveletCo. Available at http://cran.r-project.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.

Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61--78.

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

Description

Usage

Arguments

Value

References

See Also