Some comments on Hurst exponent and the long memory processes on capital markets

Granero, Miguel Ángel Sánchez; Segovia, Juan Evangelista Trinidad; Pérez, José Garcı́a

doi:10.1016/j.physa.2008.05.053

Cited by 231 publications

(78 citation statements)

References 23 publications

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“…This exponent has been widely used in the fields of hydrology, climatology, economics, geology, and geo-chemistry. The main calculation procedures are as follows (Sánchez Granero et al, 2008;Pend et (1) Divide the time series {LAI( )} ( = 1, 2, . .…”

Section: Hurst Exponentmentioning

confidence: 99%

Vegetation dynamics and responses to recent climate change in Xinjiang using leaf area index as an indicator

Guli·Jiapaer

Liang

Qian

et al. 2015

Ecological Indicators

210

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Section: Hurst Exponentmentioning

confidence: 99%

Vegetation dynamics and responses to recent climate change in Xinjiang using leaf area index as an indicator

Guli·Jiapaer

Liang

Qian

et al. 2015

Ecological Indicators

210

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“…Under the theory that the previous models and instruments need an adaptation before being exported, in a previous paper (see [20]) the authors proved that the classical methods to estimate the Hurst exponent do not work properly in short series, so they proposed a new methodology, which is based on two geometrical approaches named GM1 and GM2, that, in particular, solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series

2012

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Abstract. In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented.

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“…Geometric method-based procedures (both GM1 & GM2) were introduced in [19] and revisited afterwards in [20] to calculate the self-similarity exponent of time series. They provide two novel geometric approaches to test for scaling and correlation properties on any (financial) series.…”

Section: A Geometric Method-based Procedure: Gm2 Algorithmmentioning

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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Some comments on Hurst exponent and the long memory processes on capital markets

Cited by 231 publications

References 23 publications

Vegetation dynamics and responses to recent climate change in Xinjiang using leaf area index as an indicator

Vegetation dynamics and responses to recent climate change in Xinjiang using leaf area index as an indicator

Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series

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

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