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Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms

Detrended fluctuation analysis (DFA) is a popular method to analyze long-range temporal correlations in time series of many different research areas but in particular also for electrophysiological recordings. Using the classical DFA method, the cumulative sum of data are divided into segments, and t...

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Autores principales: Nolte, Guido, Aburidi, Mohammed, Engel, Andreas K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6474881/
https://www.ncbi.nlm.nih.gov/pubmed/31004085
http://dx.doi.org/10.1038/s41598-019-42732-7
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author Nolte, Guido
Aburidi, Mohammed
Engel, Andreas K.
author_facet Nolte, Guido
Aburidi, Mohammed
Engel, Andreas K.
author_sort Nolte, Guido
collection PubMed
description Detrended fluctuation analysis (DFA) is a popular method to analyze long-range temporal correlations in time series of many different research areas but in particular also for electrophysiological recordings. Using the classical DFA method, the cumulative sum of data are divided into segments, and the variance of these sums is studied as a function of segment length after linearly detrending them in each segment. The starting point of the proposed new method is the observation that the classical method is inherently non-stationary without justification by a corresponding non-stationarity of the data. This leads to unstable estimates of fluctuations to the extent that it is impossible to estimate slopes of the fluctuations other than by fitting a line over a wide range of temporal scales. We here use a modification of the classical method by formulating the detrending as a strictly stationary operation. With this modification the detrended fluctuations can be expressed as a weighted average across the power spectrum of a signal. Most importantly, we can also express the slopes, calculated as analytic derivatives of the fluctuations with respect to the scales, as statistically robust weighted averages across the power spectra. The method is applied to amplitudes of brain oscillations measured with magnetoencephalography in resting state condition. We found for envelopes of the the alpha rhythm that fluctuations as a function of time scales in a double-logarithmic plot differ substantially from a linear relation for time scales below 10 seconds. In particular we will show that model selections fail to determine accurate scaling laws, and that standard parameter settings are likely to yield results depending on signal to noise ratios than on true long range temporal correlations.
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spelling pubmed-64748812019-04-26 Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms Nolte, Guido Aburidi, Mohammed Engel, Andreas K. Sci Rep Article Detrended fluctuation analysis (DFA) is a popular method to analyze long-range temporal correlations in time series of many different research areas but in particular also for electrophysiological recordings. Using the classical DFA method, the cumulative sum of data are divided into segments, and the variance of these sums is studied as a function of segment length after linearly detrending them in each segment. The starting point of the proposed new method is the observation that the classical method is inherently non-stationary without justification by a corresponding non-stationarity of the data. This leads to unstable estimates of fluctuations to the extent that it is impossible to estimate slopes of the fluctuations other than by fitting a line over a wide range of temporal scales. We here use a modification of the classical method by formulating the detrending as a strictly stationary operation. With this modification the detrended fluctuations can be expressed as a weighted average across the power spectrum of a signal. Most importantly, we can also express the slopes, calculated as analytic derivatives of the fluctuations with respect to the scales, as statistically robust weighted averages across the power spectra. The method is applied to amplitudes of brain oscillations measured with magnetoencephalography in resting state condition. We found for envelopes of the the alpha rhythm that fluctuations as a function of time scales in a double-logarithmic plot differ substantially from a linear relation for time scales below 10 seconds. In particular we will show that model selections fail to determine accurate scaling laws, and that standard parameter settings are likely to yield results depending on signal to noise ratios than on true long range temporal correlations. Nature Publishing Group UK 2019-04-19 /pmc/articles/PMC6474881/ /pubmed/31004085 http://dx.doi.org/10.1038/s41598-019-42732-7 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Nolte, Guido
Aburidi, Mohammed
Engel, Andreas K.
Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title_full Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title_fullStr Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title_full_unstemmed Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title_short Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
title_sort robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6474881/
https://www.ncbi.nlm.nih.gov/pubmed/31004085
http://dx.doi.org/10.1038/s41598-019-42732-7
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