Multifractal correlation using wavelet transform modulus maxima

The wavelet transform modulus maxima method (WTMM) for a single time series is generalized to multiple time series. The new method, which is called the joint WTMM analysis in this work, allows analyses of multifractal correlation between simultaneously measured data. Dependent, partly dependent and independent binomial cascades are used to test the joint WTMM formulism and the degree of correlation assessed qualitatively is found to agree well with the theoretical predictions. Finally, the technique is applied to simultaneously measured surface scalp potential and heart rate data taken from two healthy human subjects. Via this new method, it is shown that there is multifractal correlation between the fractal dynamics in the cortex and the autonomic regulation of the heart rate.