Comparative Study of Sliding Window Multifractal Detrended Fluctuation Analysis and Multifractal Moving Average Algorithm

Abstract

Sliding window multifractal detrended fluctuation analysis (W-MFDFA) and multifractal moving average detrended method (MFDMA) are two effective methods to study multifractal characteristics of nonstationary time series. Taking the typical BMS signal model as an example, the selection of parameters, calculation accuracy and noise effects of the two algorithms are analyzed and compared. The results show that the calculation accuracy of MFDMA is better than that of W-MFDFA, but the latter is not sensitive to the changes of parameters, and has stronger anti-interference ability to noise and better stability. It can provide valuable reference for the research of actual data and the selection of internal parameters of the algorithm.

Multivariate Multifractal Detrending Moving Average Analysis of Air Pollutants

“…It is evident from the presented results that the algorithm depends on the position of the moving window. According to [24], the lowest accuracy is obtained when θ = 0.5, while θ = 0 and θ = 1 provide higher accuracy.…”

MFDFA: Efficient Multifractal Detrended Fluctuation Analysis in Python

“…The overlapping moving windows included in this library is not aimed at detrending, but instead for the analyses of rather short time series or very large scales in longer time series [8]. In the literature several applications of moving average windows have been proposed as methods to remove trends and ensure stationarity, by simply removing a windowed average to the time se-ries [8,9,42]. This is not what we do here.…”

“…Since its initial development in the late 90's, it has been revisited to incorporate several other elements, e.g. empirical mode decomposition as a method for detrending [4][5][6][7], overlapping moving windows [8,9], and a new metric denoted extended detrended fluctuation analysis [10][11][12][13]. There are several additional features exist, designed to study correlations of two or more time series [14,15], lag correlations in time series [16], and Fourier-DFA [17], amongst others.…”

Anti-Motion Interference Wearable Device for Monitoring Blood Oxygen Saturation Based on Sliding Window Algorithm

“…The third type of wearable monitoring device (flexible electronic device) is quite different from the first two types. With the development of materials science and semiconductor technology, it has the characteristics of miniaturization and flexibility, mainly including epidermal electronic equipment [37], Electronic skin [38], etc. At present, this type of wearable monitoring device is still in the research stage.…”