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

Author(s):  
Carlos Carrizales-Velazquez ◽  
Reik V. Donner ◽  
Lev Guzmán-Vargas
2021 ◽  
Author(s):  
Carlos Carrizalez-Velazquez ◽  
Reik Donner ◽  
Lev Guzmán-Vargas

Abstract We introduce a generalization of Higuchi’s estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series. The resulting multifractal Higuchi dimension anal ysis (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 as well as 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 time series.


2019 ◽  
Vol 64 (9) ◽  
pp. 7-24
Author(s):  
Grzegorz Przekota

One of the most important issues to be settled in the analysis of time series is determining their variability andidentifying the process of shaping their values. In the classical approach, volatility is most often identified with the variance of growth rates.However, risk can be characterisednot only by the variability, but also by the predictability of the changes which can be evaluatedusing thefractal dimension. The aim of this paper is to presentthe applicability of the fractal dimension estimated by the surface division method tothe assessment ofthe properties of time series. The paper presents a method for determining the fractal dimension, its interpretation, significance tables and an example of its application. Fractal dimension has been used here to describe the properties of the time series of the WIG stockexchange index in 2014–2018 and the time series of the growth rates of the largest listed Polish companiesin 2015–2018. The applied methodmakesit possible toclassify a time series into one of three classesof series: persistent, random or antipersistent. Specific cases showthe differences between the use of standard deviation and fractal dimension for riskassessment. Fractal dimension appears here to be a method for assessing the degree of stability of variations.


2018 ◽  
Vol 14 (4) ◽  
pp. 403 ◽  
Author(s):  
Srimonti Dutta ◽  
Dipak Ghosh ◽  
Sucharita Chatterjee

Fractals ◽  
2016 ◽  
Vol 24 (04) ◽  
pp. 1650046 ◽  
Author(s):  
MEIFENG DAI ◽  
SHUXIANG SHAO ◽  
JIANYU GAO ◽  
YU SUN ◽  
WEIYI SU

The multifractal analysis of one time series, e.g. crude oil, gold and exchange rate series, is often referred. In this paper, we apply the classical multifractal and mixed multifractal spectrum to study multifractal properties of crude oil, gold and exchange rate series and their inner relationships. The obtained results show that in general, the fractal dimension of gold and crude oil is larger than that of exchange rate (RMB against the US dollar), reflecting a fact that the price series in gold and crude oil are more heterogeneous. Their mixed multifractal spectra have a drift and the plot is not symmetric, so there is a low level of mixed multifractal between each pair of crude oil, gold and exchange rate series.


2015 ◽  
Vol 25 (6) ◽  
pp. 063113 ◽  
Author(s):  
Luciano Telesca ◽  
Zbigniew Czechowski ◽  
Michele Lovallo

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.


Sign in / Sign up

Export Citation Format

Share Document