Sign Retention in Classical MF-DFA

Abstract

In this paper, we propose a one-dimensional (1D) multifractal sign retention detrending fluctuation analysis algorithm (MF-S-DFA). The proposed method is based on conventional multifractal detrending fluctuation analysis (MF-DFA). As negative values may exist in the calculation in the original MF-DFA model, sign retention is considered to improve performance. We evaluate the two methods based on time series constructed by p-model multiplication cascades. The results indicate that the generalized Hurst exponent H(q), the scale exponent τ(q) and the singular spectrum f(α) estimated by MF-S-DFA behave almost consistently with the theoretical values. Moreover, we also employ distance functions such as DH and Dτ. The results prove that MF-S-DFA achieves more accurate estimation. In addition, we present various numerical experiments by transforming parameters such as nmax, q and p. The results imply that MF-S-DFA obtains more excellent performance than that of conventional MF-DFA in all cases. Finally, we also verify the high feasibility of MF-S-DFA in ECG signal classification. Through classification of normal and abnormal ECG signals, we further corroborate that MF-S-DFA is more effective than conventional MF-DFA.