Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.6
5.4
Journals
Fractal Fract
Special Issues
Modern Methods for Fractal and Multifractal Analysis of Time Series:...
share announcement

Modern Methods for Fractal and Multifractal Analysis of Time Series: Theoretical Frameworks and Practical Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 2290

Special Issue Editor

Prof. Dr. Lyudmyla Kirichenko

E-Mail Website
Guest Editor
Applied Mathematics Department, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine
Interests: deterministic chaotic systems; stochastic self-similar and multifractal processes; time series modeling and forecasting; fractal and multifractal analysis

Special Issue Information

Dear Colleagues,

Fractal analysis of time series holds significant importance and finds wide-ranging applications across various domains today due to its ability to uncover hidden patterns and complex structures inherent in temporal data. It provides a powerful framework for capturing the long-term memory and scaling properties of time series, making it invaluable in understanding the underlying dynamics of diverse systems.

The Special Issue aims to explore the cutting-edge techniques employed and advancements made in analyzing time series data using self-similar and multifractal approaches. It delves into both the theoretical underpinnings and real-world applications of these methods, highlighting their relevance and potential impact in various scientific and practical domains.

This Special Issue serves as an essential resource for researchers, practitioners, and students interested in leveraging advanced techniques to analyze time series data. By combining theoretical foundations with diverse practical applications, this volume seeks to advance the understanding and utilization of fractal methods across various disciplines.

 The scope of this Special Issue includes, but is not limited to, the following topics:

  • Theoretical concepts of fractal analysis applied to time series.
  • Innovative methodologies and algorithms for evaluating self-similarity in time series.
  • Time series multifractal analysis techniques.
  • AI-enabled analysis of time series with fractal structure: forecasting, anomaly detection, clustering, classification, and others.
  • AI-driven fractal analysis: exploring the synergy of artificial intelligence and fractal investigations.
  • Applications: economics and finance; biomedical signal processing and enhanced medical diagnostics; study of anomalous diffusion; network traffic analysis; environmental and climate science; optimizing industrial processes; interdisciplinary research.

Prof. Dr. Lyudmyla Kirichenko
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal/multifractal analysis
  • self-similarity
  • time series
  • long-term memory
  • scaling properties
  • artificial intelligence
  • applications

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

26 pages, 395 KiB  
Article
Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models
by Yuliya Mishura and Kostiantyn Ralchenko
Fractal Fract. 2024, 8(2), 79; https://doi.org/10.3390/fractalfract8020079 - 25 Jan 2024
Viewed by 822
Abstract
Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek [...] Read more.
Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes. Full article
(This article belongs to the Special Issue Modern Methods for Fractal and Multifractal Analysis of Time Series: Theoretical Frameworks and Practical Applications)
22 pages, 1188 KiB  
Article
Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers
by Juan Carlos de la Torre, Pablo Pavón-Domínguez, Bernabé Dorronsoro, Pedro L. Galindo and Patricia Ruiz
Fractal Fract. 2023, 7(11), 794; https://doi.org/10.3390/fractalfract7110794 - 30 Oct 2023
Cited by 1 | Viewed by 996
Abstract
Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a [...] Read more.
Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a single measurement is not representative of the system’s behavior. In such cases, the current multifractal detrended fluctuation analysis (MFDFA) method cannot offer confident conclusions. This work presents multi-signal MFDFA (MS-MFDFA), a novel methodology for accurately characterizing uncertain systems using the MFDFA algorithm, which enables overcoming the uncertainty of the system by simultaneously considering a large set of signals. As a case study, we consider the problem of characterizing software (Sw) consumption. The difficulty of the problem mainly comes from the complexity of the interactions between Sw and hardware (Hw), as well as from the high uncertainty level of the consumption measurements, which are affected by concurrent Sw services, the Hw, and external factors such as ambient temperature. We apply MS-MFDFA to generate a signature of the Sw consumption profile, regardless of the execution time, the consumption levels, and uncertainty. Multiple consumption signals (or time series) are built from different Sw runs, obtaining a high frequency sampling of the instant input current for each of them while running the Sw. A benchmark of eight Sw programs for analysis is also proposed. Moreover, a fully functional application to automatically perform MS-MFDFA analysis has been made freely available. The results showed that the proposed methodology is a suitable approximation for the multifractal analysis of a large number of time series obtained from uncertain systems. Moreover, analysis of the multifractal properties showed that this approach was able to differentiate between the eight Sw programs studied, showing differences in the temporal scaling range where multifractal behavior is found. Full article
(This article belongs to the Special Issue Modern Methods for Fractal and Multifractal Analysis of Time Series: Theoretical Frameworks and Practical Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop