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. 2018 Jan 13;39(4):1825–1838. doi: 10.1002/hbm.23971

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© 2018 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Step‐wise explanation of detrended fluctuation analysis. Adapted with permission from “Detrended fluctuation analysis: a scale‐free view on neuronal oscillations,” by R. Hardstone, S.S. Poil, G. Schiavone, R. Jansen, V. Nikulin, H.D. Mansvelder, and K. Linkenkaer‐Hansen, 2012, Frontiers in physiology, 3, 7. (a) Original time series. Taken from a 1/f signal sampled at 5 Hz with a duration of 100 s. (b) Cumulative sum of original signal shows large fluctuations away from the mean. (c) For each window size looked at, remove the linear trend from the signal, and then calculate the fluctuation. Signal shown as solid line and detrended signal shown as dotted line. (d) Plot the mean fluctuation per window size against window size on logarithmic axes. The DFA exponent is the slope of the best‐fit line (α = 1)