Multifractality Tests Using Bootstrapped Wavelet Leaders

Wendt, Herwig; Abry, Patrice

doi:10.1109/tsp.2007.896269

Cited by 105 publications

(95 citation statements)

References 25 publications

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“…Since then, many studies on multifractality and its applications have been continuously conducted [35]. The analysis method, namely, wavelet leaders multifractal analysis (WLMF), is a discrete version of wavelet transform modulus maxima (WTMM) method [36,37]. The DFA and WTMM methods are compared in many literatures (see, e.g., [16,24,38]).…”

Section: Introductionmentioning

confidence: 99%

Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Zhao

et al. 2017

Discrete Dynamics in Nature and Society

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We study the multifractal properties of water level with a high-frequency and massive time series using wavelet methods (estimation of Hurst exponents, multiscale diagram, and wavelet leaders for multifractal analysis (WLMF)) and multifractal detrended fluctuation analysis (MF-DFA). The dataset contains more than two million records from 10 observation sites at a northern China river. The multiscale behaviour is observed in this time series, which indicates the multifractality. This multifractality is detected via multiscale diagram. Then we focus on the multifractal analysis using MF-DFA and WLMF. The two methods give the same conclusion that at most sites the records satisfy the generalized binomial multifractal model, which is robust for different times (morning, afternoon, and evening). The variation in the detailed characteristic parameters of the multifractal model indicates that both human activities and tributaries influence the multifractality. Our work is useful for building simulation models of the water level of local rivers with many observation sites.

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Section: Introductionmentioning

confidence: 99%

Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Zhao

et al. 2017

Discrete Dynamics in Nature and Society

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“…The pointwise Hölder exponent is one of the quantifiers proposed to measure the local regularity; in fact, a low pointwise Hölder exponent reflects a highly irregular path around the point, whereas a high pointwise Hölder exponent is related to a smooth behavior. Jaffard [12] proposed a characterization of the local regularity using the wavelet coefficients obtained from the wavelet decomposition of the signal; see also [13]. Rosenblatt et al [14] studied the local regularity of a time series applying an entropy measure based on the wavelet leaders.…”

Section: Introductionmentioning

confidence: 99%

Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis

Pascoal

Monteiro

2014

Entropy

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In this study, features of the financial returns of the PSI20index, related to market efficiency, are captured using wavelet-and entropy-based techniques. This characterization includes the following points. First, the detection of long memory, associated with low frequencies, and a global measure of the time series: the Hurst exponent estimated by several methods, including wavelets. Second, the degree of roughness, or regularity variation, associated with the Hölder exponent, fractal dimension and estimation based on the multifractal spectrum. Finally, the degree of the unpredictability of the series, estimated by approximate entropy. These aspects may also be studied through the concepts of non-extensive entropy and distribution using, for instance, the Tsallis q-triplet. They allow one to study the existence of efficiency in the financial market. On the other hand, the study of local roughness is performed by considering wavelet leader-based entropy. In fact, the wavelet coefficients are computed from a multiresolution analysis, and the wavelet leaders are defined by the local suprema of these coefficients, near the point that we are considering. The resulting entropy is more accurate in that detection than the Hölder exponent. These procedures enhance the capacity to identify the occurrence of financial crashes.

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“…Recently, a new multifractal analysis method based on wavelet leaders was proposed by Lashermes, Jaffard, and Wendt [5][6][7]. Based on discrete wavelet transform (DWT), the new method has solid theoretical mathematical support and complicated calculation is avoided.…”

Section: Introductionmentioning

confidence: 99%

Wavelet Leaders Based Vibration Signals Multifractal Features of Plunger Pump in Truck Crane

Cui

et al. 2013

Advances in Mechanical Engineering

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Vibration signal of plunger pump in truck crane is a typical nonlinear, nonstationary signal, and the multifractal features are a powerful tool for depicting the geometry features of such signals. The wavelet-leaders based multifractal features extraction method is an attractive tool, which has solid theoretical mathematical support and a simplified calculation procedure. The waveletleaders based multifractal features extraction method is compared for the original signal and the denoised signal, and the statistical performance of the obtained features is also introduced based on block bootstrap technology. The effectiveness of the wavelet leaders based method is first verified for a traditional multifractal signal. Then, the application of the proposed method to the pump vibration signals of three working conditions of truck crane: lifting, rotating, and luffing is discussed. The result shows that the geometry features of vibration signals can be obtained with wavelet leaders multifractal analysis method, and the denoising process improves the multifractal features.

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Multifractality Tests Using Bootstrapped Wavelet Leaders

Cited by 105 publications

References 25 publications

Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis

Wavelet Leaders Based Vibration Signals Multifractal Features of Plunger Pump in Truck Crane

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