Deep multifractal detrended cross-correlation analysis algorithm for multifractals

Abstract

In the natural and social sciences, multifractal properties between two non-stationary time series are influenced not only by each other, but also by exogenous variables and historical data. However, traditional multifractal detrended cross-correlation analysis did not realize this problem, but directly explored the multifractal nature of time series. To eliminate the influence of exogenous variables and historical data as much as possible, the deep multifractal detrended cross-correlation analysis (DMF-DCCA) is developed to research the multifractal cross- correlation nature between two non-stationary time series. Furthermore, the effectiveness of DMF-DCCA has been validated using a simulated dataset and two real-world datasets.