Revisiting detrended fluctuation analysis

Abstract

Half a century ago Hurst introduced Rescaled Range (R/S) Analysis to study fluctuations in time series. Thousands of works have investigated or applied the original methodology and similar techniques, with Detrended Fluctuation Analysis becoming preferred due to its purported ability to mitigate nonstationaries. We show Detrended Fluctuation Analysis introduces artifacts for nonlinear trends, in contrast to common expectation, and demonstrate that the empirically observed curvature induced is a serious finite-size effect which will always be present. Explicit detrending followed by measurement of the diffusional spread of a signals' associated random walk is preferable, a surprising conclusion given that Detrended Fluctuation Analysis was crafted specifically to replace this approach. The implications are simple yet sweeping: there is no compelling reason to apply Detrended Fluctuation Analysis as it 1) introduces uncontrolled bias; 2) is computationally more expensive than the unbiased estimator; and 3) cannot provide generic or useful protection against nonstationaries.

Evaluating the Performance of Hydrological Models via Cross-Spectral Analysis: Case Study of the Thames Basin, United Kingdom

“…However, many studies have inferred a power-law character from the power spectra of monthly and annual discharge data from large basins (e.g., Pelletier and Turcotte 1997). Such an interpretation implies long-term memory associated with the Hurst phenomenon (Hurst 1951;Mesa and Poveda 1993;Heneghan and McDarby 2000;Schepers et al 1992;Bryce and Sprague 2012;Fleming 2014).…”

On the scaling effect in global surface air temperature anomalies

“…The reason we have used both annual mean and monthly mean temperature anomalies is due to the ongoing debate about the minimum allowable amount of data required to reliably employ the DFA methodology (Bryce and Sprague, 2012). Some of the earlier studies claim that DFA requires a large sample size (i.e., 1000+ data points), while others suggest a definitive minimum sample size (e.g., 600 by Ludecke et al, 2011, or less by Delignieres et al, 2006and Cororando and Carpena, 2012.…”

“…The prediction of these mechanisms is of great importance for the description of the temporal evolution of various parameters of the other subsystems of the climatic system (i.e., the hydrosphere, lithosphere, cryosphere and biosphere), given that all the sub-systems of the climate system interact between them via non-linear processes (e.g., Anthis and Cracknell, 2005;Alexandris et al, 1999;Chandra and Varotsos, 1995;Efstathiou et al, 1998Efstathiou et al, , 2003Feretis et al, 2002;Katsambas et al, 1997;Varotsos, 1995a, b, c, 1996;Melnikova, 2009;Tzanis and Varotsos, 2008;Varotsos et al, 1994;Xue et al, 2011). In other words, the temporal fluctuations of LSAT are of composite nature, consisting of periodic and non-periodic components (e.g., Chattopadhyay and Chattopadhyay, 2010;Efstathiou and Varotsos, 2010). These interactions may occur between different parts of the same subsystem.…”

Measuring long-range correlations in news flow intensity time series

“…DFA method was e®ectively applied for solving many scienti¯c and engineering problems, including analysis of DNA, [19][20][21] biomedical signal processing, 11-15 study of daily internet tra±c dynamics, 23 analysis of economical and¯nance time series, 2-6 human gait behavior. 16,17 However, DFA has some drawbacks 43 : DFA can lead to uncontrolled bias; DFA is more expensive than unbiased estimator; DFA cannot provide protection against nonlinear nonstationaries.…”