An accurate algorithm to calculate the Hurst exponent of self-similar processes

Fernández–Martínez, M.; Sánchez-Granero, M.A.; Segovia, Juan Evangelista Trinidad; Sánchez, Isabel María Román

doi:10.1016/j.physleta.2014.06.018

Cited by 27 publications

(21 citation statements)

References 43 publications

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“…As well as it happens with other tools to test for scaling properties of time series (see for example, MF-DFA [ 76 ], MF-DMA [ 63 ] and FD4 [ 77 ]), GHE provides a valid procedure to deal with multi-fractal (also multi-scaling) processes, namely, those ones in which the scaling exponent H ( q ) depends on each moment q . In such case, different exponents characterize the scaling properties of different q th-moments for the underlying distribution [ 78 , 79 ].…”

Section: Methodsmentioning

confidence: 99%

The Effect of the Underlying Distribution in Hurst Exponent Estimation

et al. 2015

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In this paper, a heavy-tailed distribution approach is considered in order to explore the behavior of actual financial time series. We show that this kind of distribution allows to properly fit the empirical distribution of the stocks from S&P500 index. In addition to that, we explain in detail why the underlying distribution of the random process under study should be taken into account before using its self-similarity exponent as a reliable tool to state whether that financial series displays long-range dependence or not. Finally, we show that, under this model, no stocks from S&P500 index show persistent memory, whereas some of them do present anti-persistent memory and most of them present no memory at all.

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Section: Methodsmentioning

confidence: 99%

The Effect of the Underlying Distribution in Hurst Exponent Estimation

et al. 2015

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“…For the sake of verifying the fractal nature in the BS topology, the rescaled range analysis (R/S) method [17] is adopted to compute the Hurst coefficients of all the selected cities in this letter. Due to the space limitation, the details about the calculation of the Hurst coefficients will not be provided here, and all the relevant information can be found in [7].…”

Section: B Fractal Features Based On the Hurst Coefficientsmentioning

confidence: 99%

Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology

Chen

Zhao

et al. 2019

IEEE Wireless Commun. Lett.

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In recent decades, the deployments of cellular networks have been going through an unprecedented expansion. In this regard, it is beneficial to acquire profound knowledge of cellular networks from the view of topology so that prominent network performances can be achieved by means of appropriate placements of base stations (BSs). In our researches, practical location data of BSs in eight representative cities are processed with classical algebraic geometric instruments, including α-Shapes, Betti numbers, and Euler characteristics. At first, the fractal nature is revealed in the BS topology from both perspectives of the Betti numbers and the Hurst coefficients. Furthermore, lognormal distribution is affirmed to provide the optimal fitness to the Euler characteristics of real BS deployments.

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“…This makes a GHE based analysis quite simple to test for scaling properties on time series. As well as it happens with other approaches to test for scaling properties on series (see e.g., MF-DFA [17] as well as FD algorithms [8]), GHE provides an appropriate procedure to deal with multi-fractal (also multi-scaling) processes, namely, those ones for which the scaling exponent H(q) depends on each qth-order moment. In such a case, different exponents characterize the scaling properties for distinct qth-order moments on the underlying distribution [6,21].…”

Section: Generalized Hurst Exponentmentioning

confidence: 99%

A COMPARISON OF THREE HURST EXPONENT APPROACHES TO PREDICT NASCENT BUBBLES IN S&P500 STOCKS

et al. 2017

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In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior (HB) and hence, to find out the beginning of a market bubble. In particular, classical Detrended Fluctuation Analysis (DFA), Generalized Hurst Exponent (GHE) and GM2 (one of Geometric Method-based algorithms) were applied for self-similarity exponent calculation purposes. Traditionally, researchers have been focused on identifying the beginning of a crash. Instead of this, we are pretty interested in identifying the beginning of the transition process from EM to a market bubble onset, what we consider could be more interesting. The relevance of self-similarity index in such a context lies on the fact that it becomes a suitable indicator which allows to identify the raising of HB in financial markets. Overall, we could state that the greater the self-similarity exponent in financial series, the more likely the transition process to HB could start. This fact is illustrated through actual S&P500 stocks.

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An accurate algorithm to calculate the Hurst exponent of self-similar processes

Cited by 27 publications

References 43 publications

The Effect of the Underlying Distribution in Hurst Exponent Estimation

The Effect of the Underlying Distribution in Hurst Exponent Estimation

Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology

A COMPARISON OF THREE HURST EXPONENT APPROACHES TO PREDICT NASCENT BUBBLES IN S&P500 STOCKS

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