Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Abstract

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and Centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain “The Methods of Choice” in determining the Hurst index of time series.

Detrending moving average algorithm: Frequency response and scaling performances

“…Our results have demonstrated that the performance of mth order centered DMA, where m is a nonnegative even integer, is very well comparable with that of (m + 1)th order DFA. It has been demonstrated that the zeroth order centered DMA has a good performance to characterize long-range correlation and fractal scaling behavior [28,34]. In practical applications to real-world time series, the higher detrending power degree would be very important to improve estimation accuracy and to validate the observed scaling behavior [41,42].…”

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

“…Until now various methods have been developed and applied to characterize the correlation behavior on many time series starting from R/S analysis [4][5][6][7], detrended fluctuation analysis (DFA) [8][9][10], detrended moving average method (DMA) [11], multifractal detrended fluctuation analysis (MFDFA) [12], wavelet based fluctuation analysis (WBFA) [13][14][15][16], average wavelet coefficient method (AWC) [17], wavelet transform modulus maxima (WTMM) [18] etc. These methods have found wide application in the analysis of correlations and characterization of scaling behavior of time-series data in physiology, finance, and natural sciences [19][20][21][22][23][24][25][26][27][28][29].…”

Magnetic resonance image segmentation using multifractal techniques

“…The MF-DMA family gives better scaling behavior in many cases [9,31]. We intent to perform MF-DMS-based method to compare the presented results obtained with the MF-DFS to get best segmentation results in our next study.…”