Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences

Likens, Aaron D.; Mangalam, Madhur; Wong, Aaron Y.; Charles, Anaelle C.; Mills, Caitlin

doi:10.48550/arxiv.2301.11262

Cited by 3 publications

(5 citation statements)

References 134 publications

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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%

“…We previously compared the performance of the HK method and the DFA using simulated and empirical time series [63]. Using synthetic time series with a priori known values of H, we demonstrated that the HK method consistently outperforms DFA in three ways.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing a Bayesian method for estimating the Hurst exponent in behavioral sciences

Mangalam¹,

Wilson²,

Sommerfeld³

et al. 2023

Preprint

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The Bayesian Hurst-Kolmogorov (HK) method estimates the Hurst exponent of a time series more accurately than the age-old detrended fluctuation analysis (DFA), especially when the time series is short. However, this advantage comes at the cost of computation time. The computation time increases exponentially with N , easily exceeding several hours for N = 1024, limiting the utility of the HK method in real-time paradigms, such as biofeedback and brain-computer interfaces. To address this issue, we have provided data on the estimation accuracy of H for synthetic time series as a function of a priori known values of H, the time series length, and the simulated sample size from the posterior distribution-a critical step in the Bayesian estimation method. The simulated sample from the posterior distribution as small as n = 25 suffices to estimate H with reasonable accuracy for a time series as short as 256 measurements. Using a larger simulated sample from the posterior distribution-i.e., n > 50-provides only marginal gain in accuracy, which might not be worth trading off with computational efficiency. We suggest balancing the simulated sample size from the posterior distribution of H with the computational resources available to the user, preferring a minimum of n = 50 and opting for larger sample sizes based on time and resource constraints.

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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%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing a Bayesian method for estimating the Hurst exponent in behavioral sciences

Mangalam¹,

Wilson²,

Sommerfeld³

et al. 2023

Preprint

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show abstract

“…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%

Chance or Chaos? Fractal Geometry Aimed to Inspect the Nature of Bitcoin

Cabezas-Rivas,

Sánchez-Coll,

Tormo-Xaixo

2023

Fractal Fract

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The aim of this paper is to analyse Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75% of total market capitalisation and compare their evolution with that of a wide variety of traditional assets: commodities with spot and future contracts, treasury bonds, stock indices, and growth and value stocks. Fractal geometry will be applied to carry out a careful statistical analysis of the performance of Bitcoin returns. As a main conclusion, we have detected a high degree of persistence in its prices, which decreases the efficiency but increases its predictability. Moreover, we observe that the underlying technology influences price dynamics, with fully decentralised cryptocurrencies being the only ones to exhibit self-similarity features at any time scale.

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“…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%

NONAN GaitPrint: An IMU gait database of healthy young adults

Wiles,

Mangalam,

Sommerfeld

et al. 2023

Sci Data

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An ongoing thrust of research focused on human gait pertains to identifying individuals based on gait patterns. However, no existing gait database supports modeling efforts to assess gait patterns unique to individuals. Hence, we introduce the Nonlinear Analysis Core (NONAN) GaitPrint database containing whole body kinematics and foot placement during self-paced overground walking on a 200-meter looping indoor track. Noraxon Ultium MotionTM inertial measurement unit (IMU) sensors sampled the motion of 35 healthy young adults (19–35 years old; 18 men and 17 women; mean ± 1 s.d. age: 24.6 ± 2.7 years; height: 1.73 ± 0.78 m; body mass: 72.44 ± 15.04 kg) over 18 4-min trials across two days. Continuous variables include acceleration, velocity, position, and the acceleration, velocity, position, orientation, and rotational velocity of each corresponding body segment, and the angle of each respective joint. The discrete variables include an exhaustive set of gait parameters derived from the spatiotemporal dynamics of foot placement. We technically validate our data using continuous relative phase, Lyapunov exponent, and Hurst exponent—nonlinear metrics quantifying different aspects of healthy human gait.

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Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences

Cited by 3 publications

References 134 publications

Optimizing a Bayesian method for estimating the Hurst exponent in behavioral sciences

Optimizing a Bayesian method for estimating the Hurst exponent in behavioral sciences

Chance or Chaos? Fractal Geometry Aimed to Inspect the Nature of Bitcoin

NONAN GaitPrint: An IMU gait database of healthy young adults

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