Generalization of Higuchi’s fractal dimension for multifractal analysis of time series with limited length

被引:0
作者
Carlos Carrizales-Velazquez
Reik V. Donner
Lev Guzmán-Vargas
机构
[1] Instituto Politécnico Technology,Unidad Profesional Interdisciplinaria en Ingeniería y Tecnología Avanzada
[2] Instituto Politécnico Nacional,Department of Water, Environment, Construction and Safety
[3] Magdeburg-Stendal University of Applied Sciences,Research Department I – Earth System Analysis & Research Department IV – Complexity Science
[4] Potsdam Institute of Climate Impact Research (PIK) – Member of the Leibniz Association,undefined
来源
Nonlinear Dynamics | 2022年 / 108卷
关键词
Fractal dimension; Higuchi method; Multifractal spectrum; Partition function; Stochastic processes; Word lengths;
D O I
暂无
中图分类号
学科分类号
摘要
There exist several methodologies for the multifractal characterization of nonstationary time series. However, when applied to sequences of limited length, these methods often tend to overestimate the actual multifractal properties. To address this aspect, we introduce here a generalization of Higuchi’s estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series or sequences of relatively short length. This multifractal Higuchi dimension analysis (MF-HDA) method considers the order-q moments of the partition function provided by the length of the time series graph at different levels of subsampling. The results obtained for different types of stochastic processes, a classical multifractal model, and various real-world examples of word length series from fictional texts demonstrate that MF-HDA provides a reliable estimate of the multifractal spectrum already for moderate time series lengths. Practical advantages as well as disadvantages of the new approach as compared to other state-of-the-art methods of multifractal analysis are discussed, highlighting the particular potentials of MF-HDA to distinguish mono- from multifractal dynamics based on relatively short sequences.
引用
收藏
页码:417 / 431
页数:14
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