2023
DOI: 10.48550/arxiv.2301.11262
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Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences

Abstract: Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, $H$. Specifically, DFA quantifies the linear regression slope in log-log coordinates representing the relationship between the time series' variability and the number of timescales over which this variability is computed. We compared the performance of two methods of fractal analysis -- the current gold standard, … Show more

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Cited by 3 publications
(5 citation statements)
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“…The HK method offers several advantages over DFA in estimating the Hurst exponent of a time series [63]. However, these advantages come at the cost of computation time.…”
Section: Discussionmentioning
confidence: 99%
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“…The HK method offers several advantages over DFA in estimating the Hurst exponent of a time series [63]. However, these advantages come at the cost of computation time.…”
Section: Discussionmentioning
confidence: 99%
“…As noted above, a recently introduced Bayesian approach to estimating H [62] shows remarkable promise in addressing fundamental limitations with DFA. In previous work, we have demonstrated that the HK method outperforms DFA in several contexts [63]. Our current interest is investigating the HK method's performance trade-offs related to computational efficiency.…”
Section: Methodsmentioning
confidence: 99%
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“…In short, while methodological enhancements and the theoretical backup for DFA are developed, we will double check the stationarity of our series, and we opted for the R/S method, which has very recently been applied in similar settings by [10]. Let us finally point out that the search of new methods to beat DFA is an active topic of research, including Bayesian methods [64], wavelet analysis [21] or deep learning models [22].…”
Section: Justification Of the Chosen Methodology: R/s Versus Dfamentioning
confidence: 99%
“…We assessed the strength of long-range correlations in the time series of stride length and stride time following the Bayesian approach developed by Tyralis and Koutsoyiannis 143 . We chose this method because it performs well on short time series, as compared to more common methods like detrended fluctuation analysis 144,145 , which requires much longer time series data, and yields H fGn comparable to the more commonly used detrended fluctuation analysis 146 .…”
Section: Continuous Phase Relationship Between the Right And Left Lim...mentioning
confidence: 99%