Fully multivariate detrended fluctuation analysis using Mahalanobis norm with application to multivariate signal denoising

Abstract

Detrended fluctuation analysis (DFA) has become an important tool for the long-range correlation and local regularity fluctuation analysis of nonstationary time series data. While the method is well-established and well-understood for single time series data, its extensions for multivariate data (comprising multiple channels) are still emerging. A major challenge in that regard is to incorporate inherent inter-channel dependencies within the DFA analysis. We propose a novel method to address that challenge through Mahalanobis distance (MD) norm that provides an analytical way to incorporate covariance matrix within the computation of the proposed multichannel fluctuation function. Through analytical analysis and experimental results, we show that incorporation of cross-channel correlations within the fluctuation function makes the rendered long-range correlation analysis more accurate for the multivariate correlated data. Next, we next demonstrate the utility of the proposed generic multichannel DFA (GMDFA) within the multivariate signal denoising problem(s). To this end, our denoising approach first obtains data driven multiscale signal representation by multi-stage use of multivariate variational mode decomposition (MVMD) method. Then, proposed GMDFA is used to reject the predominantly noisy modes based on their randomness scores.