Wavelet packet computation of the Hurst exponent

Jones, Cameron L.; Lonergan, Greg T.; Mainwaring, David E.

doi:10.1088/0305-4470/29/10/029

Cited by 42 publications

(26 citation statements)

References 27 publications

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“…* Ingve.Simonsen@phys.ntnu.no † Alex.Hansen@phys.ntnu.no ‡ Olav-Magnar. Nes@iku.sintef.no To our knowledge, two papers discuss wavelet based techniques in connection with Hurst exponent measurements [8,9]. In [8], the wavelet transform modulus maxima method is introduced, and in [9], wavelet packet analysis is used to extract the Hurst exponent.…”

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confidence: 99%

Determination of the Hurst exponent by use of wavelet transforms

Simonsen

Hansen

Nes³

1998

Phys. Rev. E

244

151

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We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared to those obtained with Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin. * Ingve.Simonsen@phys.ntnu.no † Alex.Hansen@phys.ntnu.no ‡ Olav-Magnar. Nes@iku.sintef.no To our knowledge, two papers discuss wavelet based techniques in connection with Hurst exponent measurements [8,9]. In [8], the wavelet transform modulus maxima method is introduced, and in [9], wavelet packet analysis is used to extract the Hurst exponent. The method we present here differs from both of these. We would also like to mention two other papers which discuss self-affine fractals by using wavelets [10,11]. However, these two papers are mainly concerned about the so-called inverse fractal problem for self-affine fractals and not measuring of Hurst exponents. This paper is organized as follows. In Sec. II we review the central properties of self-affine surfaces, while in Sec. III the wavelet transform is reviewed. Sec. IV presents the derivation of the scaling relation for self-affine functions in the wavelet domain. In Sec. V this scaling relation is applied to synthetic and experimental data, and Hurst exponents are extracted. Finally, in Sec. VI, our conclusion is presented.

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confidence: 99%

Determination of the Hurst exponent by use of wavelet transforms

Simonsen

Hansen

Nes³

1998

Phys. Rev. E

244

151

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“…The first results that are particularly relevant come from the log-energy plot obtained with the WP coefficient sequences, compared to the corresponding variance plot. A linearly decreasing behavior for the highest scales is followed by an upward step when resolution level 4 appears, and then a new jump occurs at level 6. This behavior is in part expected, being the scaling effects observed usually in a limited range h See Jones et al 25 for a study of WP and the computation of the Hurst exponent. of scales.…”

Section: Empirical Applicationmentioning

confidence: 69%

Exploring Multi-Resolution and Multi-Scaling Volatility Features

Capobianco¹

2004

Fractals

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One of the most recent results in empirical finance is the achievement of an accuracy gain for the volatility estimates from the use of high-frequency samples. In many applications, for instance, the observed intra-day data become the best informative source of estimation for the daily volatilites. This information set, or filtration in probability terms, can in theory be optimally exploited while adopting an increasingly finer sampling rate, a fact which finds justification when assuming a stochastic characterization of the problem in terms of so-called semimartingales. These instruments are very useful for representing asset price dynamics, and in recent proposals supply realized and integrated volatility measures. The former volatility is the empirical approximation of the latter, an average of high frequency returns observed within a certain time frame. Semimartingales become suitable model tools by allowing for the quadratic variation principle to hold. This in turn means that the convergence of the realized to the integrated volatility can be verified; conversely, from both theoretical and experimental standpoints, the cumulative squared high frequency returns represent consistent estimators of the integrated volatility measure. The goal of this work is twofold: first, to show with simulations the quality of the convergence for time-based estimators, compared to that obtained when time-scale coordinate wavelet tranforms are considered. Second, to verify that special families of wavelet decompose returns and allow for multi-scaling features to be revealed, together with the possible presence of underlying nonlinear dynamics of stock index return volatility.

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“…Proposed time-scale techniques by the wavelet transform are implemented (Eke et al, 2002; Audit et al, 2002; Jones et al, 1999; Simonsen et al, 1998; Veitch and Abry, 1999; Arneodo et al, 1996). The Average Wavelet Coefficient (AWC) method described by Simonsen and Hansen (Simonsen et al, 1998) is conveniently implemented for this function.…”

Section: Algorithms For Estimation Of β Valuesmentioning

confidence: 99%

A comparative analysis of spectral exponent estimation techniques for 1/fβ processes with applications to the analysis of stride interval time series

Schaefer

Brach

Perera

et al. 2014

Journal of Neuroscience Methods

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Background The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f) = 1/fβ. The scaling exponent β is thus often interpreted as a “biomarker” of relative health and decline. New Method This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. Results The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Comparison with Existing Methods: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. Conclusions The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series.

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Wavelet packet computation of the Hurst exponent

Cited by 42 publications

References 27 publications

Determination of the Hurst exponent by use of wavelet transforms

Determination of the Hurst exponent by use of wavelet transforms

Exploring Multi-Resolution and Multi-Scaling Volatility Features

A comparative analysis of spectral exponent estimation techniques for 1/fβ processes with applications to the analysis of stride interval time series

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