Hurst Exponent and its Applications in Time-series Analysis

Resta, Marina

doi:10.2174/2213275911205030211

Cited by 16 publications

(15 citation statements)

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“…Respecto a la última prueba, el coeficiente de Hurst se caracteriza por poseer una metodología relacionada más con la estimación que con el cálculo (Resta, 2012), lo que implica que mediante diversas metodologías pueden obtenerse valores distintos, además, que el nivel de memoria de la serie suele disminuir con la longitud de la misma (Peters, 2015). Durante el presente trabajo se aplica la variante propuesta por Andrew Lo (1991), la cual incorpora la autocorrelación para el reescalamiento de los datos, procurando así evidenciar relaciones de la serie con sus respectivos rezagos, aun cuando esta puede poseer un tamaño alto.…”

Section: Discussionunclassified

Evaluación de la hipótesis de eficiencia débil y análisis de causalidad en las centrales de abastos de Colombia

Sarmiento¹,

Lamos-Díaz²,

Hernández³

2019

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En Colombia existen centros tradicionales de acopio donde se comercializan y distribuyen productos agrícolas. El precio de venta de estos productos es publicado por instituciones del Gobierno en informes semanales. Con el objetivo de determinar si las series de precios siguen una caminata aleatoria y si existen relaciones entre los centros, se aplican seis pruebas que evalúan la hipótesis de eficiencia débil y la prueba de causalidad de Granger. Para ello se analiza el precio histórico semanal de 28 productos agrícolas comercializados en seis mercados, durante la primera semana de 2013 a la última de 2017. Los principales resultados indican que los mercados tienden a la eficiencia, aunque no tienen el mismo nivel, ya que esta varía según el producto que se comercialice. Además, los centros en Manizales, Barranquilla y Villavicencio influyen sobre los precios de los mercados de Bogotá, Bucaramanga y Medellín

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Section: Discussionunclassified

Evaluación de la hipótesis de eficiencia débil y análisis de causalidad en las centrales de abastos de Colombia

Sarmiento¹,

Lamos-Díaz²,

Hernández³

2019

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“…(DFA) DFA [39] is used for quantifying the SST of a non-stationary time series [27], [40]. For computing H using DFA technique, a time series of length K is first integrated.…”

Section: B Detrended Fluctuation Analysismentioning

confidence: 99%

A Hurst-based Diffusion Model using Time Series Characteristics for Influence Maximization in Social Networks

Chamola

Saxena

et al. 2023

Preprint

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Online Social Networks (OSNs) have grown exponentially in the last few years due to their applications in real life like marketing, recommendation systems, and social awareness campaigns. One of the most important research areas in this field is Influence Maximization (IM). IM pertains to finding methods to maximize the spread of information (or influence) across a social network. Previous works in IM have focused on using a pre-defined edge propagation probability or using the Hurst exponent (H) to identify which nodes to be activated. This is calculated on the basis of self-similarity in the time series depicting a user’s (node) past temporal interaction behaviour. In this work, we propose a Time Series Characteristic based Hurst-based Diffusion Model (TSC-HDM). The model calculates Hurst Exponent (H) based on the stationary or non-stationary characteristic of the time series. Furthermore, our model selects a handful of seed nodes and activates every seed node’s inactive successor only if H>0.5 . The process is continued until the activation of successor nodes is not possible. The proposed model was tested on 4 datasets - UC Irvine messages, Email EU-Core, Math Overflow 3, and Linux Kernel mailing list. We have also compared the results against 4 other Influence Maximisation models - Independent Cascade (IC), Weighted Cascade (WC), Trivalency (TV), and Hurst-based Influence Maximisation (HBIM). Our model achieves as much as 590% higher expected influence spread as compared to the other models. Moreover, our model attained 344% better average influence spread than other state-of-the-art models.

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“…We used the rescaled range analysis of Hurst (Resta, 2012), corrected for small sample bias (Anis and 163 Lloyd, 1976;Peters, 1994;Weron, 2002), applied to the squared timeseries for each voxel.…”

Section: Estimation Of the Hurst Exponent 162mentioning

confidence: 99%

“…;Grech and Mazur, 2004;Gao et al, 2007;Resta, 2012; 332Eftaxias et al, 2013). 333 Importantly, the HE measure is providing a different kind of information to standard measures such 334 as kurtosis.…”

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confidence: 99%

Rogue bioelectrical waves in the brain: the Hurst exponent as a potential measure for presurgical mapping in epilepsy

et al. 2019

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Objective. Brain electromagnetic activity in patients with epilepsy is characterized by abnormal high-26 amplitude transient events (spikes) and abnormal patterns of synchronization of brain rhythms that 27 accompany epileptic seizures. With the aim of improving methods for identifying epileptogenic sources in magnetoencephalographic (MEG) recordings of brain data, we applied methods 29 previously used in the study of oceanic 'rogue waves' and other freak events in complex systems 30 Approach. For data from 3 patients who were awaiting surgical treatment for epilepsy, we used a 31 beamformer source model to produce volumetric maps showing areas with a high proportion of 32 spikes that could be classified as 'rogue waves', and areas with high Hurst Exponent (HE). The HE 33 describes the extent to which a system is exhibiting persistent behavior, may predict the likelihood 34 of freak events. These measures were compared with the more standard measure of kurtosis, 35 which has been shown to be a reliable method for localizing interictal spikes. 36 Main Results. There was partial concordance between the 3 different volumetric maps indicating 37 that each measure provides different information about the underlying brain data. The HE, when 38 combined with a simple connectivity analysis based on phase slope index, was able to identify the 39 probable epileptogenic zone in all 3 patients, despite very different patterns of abnormal activity. 40 The differences between distributions of high HE and high kurtosis values indicates that while spikes 41 are propagated through cortex from the epileptogenic zone, the persistent dynamical conditions 42 under which the spikes are generated may not be propagated in a similar way. Finally, the patterns 43 of persistent activity, indicating a departure from 'healthy criticality' in brain networks may explain 44 the wide range of social and cognitive impairments that are seen in epilepsy patients. 45 Significance. The HE is a potentially useful addition to the clinician's battery of measures which may 46 be used convergently to guide surgical intervention.

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Hurst Exponent and its Applications in Time-series Analysis

Cited by 16 publications

References 0 publications

Evaluación de la hipótesis de eficiencia débil y análisis de causalidad en las centrales de abastos de Colombia

Evaluación de la hipótesis de eficiencia débil y análisis de causalidad en las centrales de abastos de Colombia

A Hurst-based Diffusion Model using Time Series Characteristics for Influence Maximization in Social Networks

Rogue bioelectrical waves in the brain: the Hurst exponent as a potential measure for presurgical mapping in epilepsy

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