Abstract
The paper considers a generalized approach to the time series multifractal analysis. The focus of research is on the correct estimation of multifractal characteristics from short time series. Based on numerical modeling and estimating, the main disadvantages and advantages of the sample fractal characteristics obtained by three methods: the multifractal fluctuation detrended analysis, wavelet transform modulus maxima and multifractal analysis using discrete wavelet transform are studied. The generalized Hurst exponent was chosen as the basic characteristic for comparing the accuracy of the methods. A test statistic for determining the monofractal properties of a time series using the multifractal fluctuation detrended analysis is proposed. A generalized approach to estimating the multifractal characteristics of short time series is developed and practical recommendations for its implementation are proposed. A significant part of the study is devoted to practical applications of fractal analysis. The proposed approach is illustrated by the examples of multifractal analysis of various real fractal time series.
Highlights
In the last years, there has been a growing interest in complex systems that have a fractal structure: informational, biological, physical, technological, financial and other
The work has considered the features of the numerical implementation of multifractal analysis methods: multifractal detrended fluctuation analysis, wavelet transform modulus maxima, multifractal analysis using discrete wavelet transform
The properties of generalized Hurst exponent estimates obtained by these methods from short time series have been investigated
Summary
There has been a growing interest in complex systems that have a fractal structure: informational, biological, physical, technological, financial and other. The dynamics of such systems generate time series with fractal (self-similar) properties. Time series fractal analysis is used to simulate, analyze and control complex systems in various fields [1]-[5]. Processes with fractal properties can be divided into two groups: monofractal and multifractal. Monofractal processes are homogeneous in the sense of fractal properties and have single scaling exponent. Multifractal processes have heterogeneous scale properties and are characterized by a set of scaling exponents
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
