Multiscale multifractal detrended fluctuation analysis of multivariate time series

This work extends the multivariate multifractal detrended fluctuation analysis(MV-MFDFA) method to multiscale case, named multiscale multivariate multifractal detrended fluctuation analysis (MMV-MFDFA). The benefits of the proposed approach are illustrated by numerical simulations on synthetic multivariate processes. Furthermore, the proposed MMV-MFDFA method is applied to the fractal auto-correlation analysis of six pollutants’ (PM2.5, PM10, SO2, NO2, CO and O3) hourly data in different seasons. The results show that the seasonal periodicity has robust impact on the auto-correlation of pollutants in spring and summer. Besides, we also find that the pollutants in the four seasons possess strong multifractal auto-correlation nature, even after the removal of the seasonal pattern. Finally, the source of multifractality among more than two series is also discussed, and some interesting results are obtained. PM2.5 not only dominates the underlying evolution process in fall and winter, but also is more correlated to the other pollutants than the other ones to each other except in spring. The proposed MMV-MFDFA methodology can provide reliable ways of measuring the fractal auto-correlation properties of multivariate series, and it can be applied to any system with multiple data channels. •Multiscale multivariate multifractal detrended fluctuation analysis method (MMV-MFDFA) is proposed.•The proposed methodology provides more convincing results than MV-MFDFA.•The newly methodology is applied to investigate the pollutants series in different seasons.•The intersurface distance is introduced to measure the difference of two Hurst surfaces.•The source of multifractality among more than two series is investigated.