# Partial Wavelet Coherence and Multiple Wavelet Coherence

Wavelet has increasingly become a common tool for time series examination in the field of geophysics. We contribute towards the documentation of its applications by writing a paper to demonstrate the geophysical applications of partial wavelet coherence and multiple wavelet coherence (Ng and Chan 2012). A software package for these wavelet techniques is developed with the paper, which is freely available on this website. The package also includes modified software for wavelet power spectrum and wavelet cross spectrum that have the bias problem rectified (Liu et al. 2007; Veleda et al. 2012).

 What is wavelet? Wavelet is a tool that allows one to determine dominant modes of variability and the change of those modes with time (Torrence and Compo 1998). Traditional mathematics methods, such as Fourier transform, examine periodicity of phenomena by assuming they are stationary in time. Wavelet, however, decomposes time series into a time-frequency space and thus be able to extract localized intermittent periodicities (Grinsted et al. 2004). It is therefore particular useful in analyzing non-stationary time series. NewsJul 2012Our paper on the applications of partial wavelet coherence and multiple wavelet coherence in geophysics has been accepted by JTECH!Jun 2012 Wavelet Matlab software package version v1.0 released!
What are partial wavelet coherence and multiple wavelet coherence?

Partial wavelet coherence is a technique similar to partial correlation that helps identify the results wavelet coherence between two time series after eliminating the influence of their common dependence. Multiple wavelet coherence, akin to multiple correlation, is useful in seeking the resulting wavelet coherence of multiple independent variables on a dependent one (Ng and Chan 2012).

What is the bias problem?

A bias problem towards low-frequency oscillations is found to be existed in the estimate of wavelet power spectra. For example, a time series that comprises of sine waves with different periods but same amplitudes does not produce identical peaks (Liu et. al. 2007). Similar problem exists in wavelet cross spectrum (Veleda et al. 2012). This bias problem has been corrected in our software.

Should there be any enquiry, please feel free to contact:

Eric K. W. Ng
Email: E.Ng@cityu.edu.hk