Multifractal temporally weighted detrended fluctuation analysis and its application in the analysis of scaling behavior in temperature series

Abstract

Detrended fluctuation analysis (DFA) is a method widely used

Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice

“…The MF-DFA was designed to estimate the scale-dependent exponent g in non-stationary time-series data containing longterm trends, and has been successful in revealing the multi-fractal structure of geophysical phenomena (Kantelhardt et al 2002). The MF-TWDFA is a variant of the MF-DFA improving the robustness of extracting the scaling of fluctuations (Zhou and Leung 2010). In the MF-TWDFA, our focus lies on the scaling law represented as~a ( )…”

“…We utilize a proven methodology called multifractal temporally weighted detrended fluctuation analysis (MF-TWDFA) (Koscielny-Bunde et al 2006, Zhou andLeung 2010, Agarwal et al 2012) to characterize the wind-blown redistribution of snow on smooth FYI and establish the physical length scales induced by wind. The methodology is particularly suited to our application as it minimizes the impact of non-stationarity in snow thickness data when characterizing the scaling behavior of correlations.…”

“…The MF-TWDFA is a modified, extended version of multifractal detrended fluctuation analysis (MF-DFA) (Kantelhardt et al 2002. The MF-TWDFA uses a weighted regression approach and hypothesizes that, in any discrete time series, points closer in time are more likely to be related than distant points (Zhou and Leung 2010). The MF-DFA is designed to erase the non-stationary trends as much as possible and reveal the auto-correlated characteristics of stationary fluctuations.…”

Multifractal scaling properties of global land surface air temperature

“…Compared with traditional methods, such as DFA and R/S (rescaled range) analysis, MFDFA identifies the scaling of the q th -order moments of the time series and can handle not only stationary but also non-stationary time series with unsure noise and trend [14,15]. Thus, it is used in this study.…”

Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation

“…As an effective way to solve the problem of nonstationary, multifractal detrended fluctuation analysis (MF-DFA) was proposed by Kantelhardt et al [18] in 2002. Because the MF-DFA does not require the modulus maxima procedure in contrast to the method of wavelet transform modulus maxima (WTMM) [17], the MF-DFA and its various modified version have been proposed for resolving various non-stationary series in lots of fields [11,12,16,20,29]. Since the new idea of the method has been employed in these fields, the MF-DFA is maturing.…”