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Fractal Fract
Special Issues
Multifractal and Time Series Analysis: Theory and Applications
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Multifractal and Time Series Analysis: Theory and Applications

A Special Issue of Fractal and Fractional (ISSN 2504-3110) belonging to the section "Complexity".

Deadline for manuscript submissions: 31 August 2027 | Viewed by 197

Editor

Prof. Dr. Fernando Henrique Antunes De Araújo

E-Mail Website
Guest Editor
Federal Institute of Education Science and Technology of Paraíba (IFPB), Patos 58700-030, Brazil
Interests: probability; mathematical statistics; statistical physics; applied probability; applied statistics; applied mathematics; information theory; multifractal analysis; data analysis; time series analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractal and multifractal methods provide a powerful framework for investigating complex systems characterized by scaling behavior, self-similarity, long-range dependence, nonlinear interactions, intermittency, and heterogeneous dynamics across temporal and spatial scales. These approaches reveal structures that conventional linear and single-scale methods may not adequately capture.

This Special Issue welcomes theoretical, methodological, computational, and empirical contributions advancing fractal, multifractal, fractional, and complexity-based analyses. We invite original research articles and reviews addressing the development, validation, comparison, and application of these methods to time series, spatial patterns, networks, images, signals, and other complex data structures.

The scope is interdisciplinary and encompasses applications in mathematics, physics, econophysics, economics, finance, engineering, energy systems, geosciences, hydrology, environmental and climate sciences, biology, medicine, neuroscience, information theory, network science, and the social sciences.

Topics of interest include, but are not limited to, fractal and multifractal models, multifractal detrended fluctuation analysis, scaling laws, fractional dynamics, nonlinear systems, complex networks, regime changes, forecasting, risk analysis, and machine-learning methods informed by fractal properties. Contributions emphasizing methodological robustness, statistical validation, reproducibility, interpretability, and innovative real-world applications are particularly encouraged.

This Special Issue seeks to strengthen the connections among mathematical foundations, computational innovation, and interdisciplinary applications of fractal and multifractal analysis.

Prof. Dr. Fernando Henrique Antunes De Araújo
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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 analysis
  • multifractal analysis
  • fractional dynamics
  • complex systems
  • complex time series
  • scaling laws
  • long-range dependence
  • nonlinear dynamics
  • multifractal detrended fluctuation analysis
  • complex networks
  • econophysics
  • interdisciplinary applications

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Published Papers (1 paper)

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Research

28 pages, 8927 KB  
Article
El Niño, La Niña, and Tropical Atlantic Signatures in Multifractal Wind-Speed Stability: Rolling Evidence from Paraíba, Brazil
by Fernando Henrique Antunes de Araujo, Kerolly Kedma Felix do Nascimento and Fábio Sandro dos Santos
Fractal Fract. 2026, 10(10), 663; https://doi.org/10.3390/fractalfract10100663 (registering DOI) - 23 Sep 2026
Abstract
This paper examines the multifractal organization of hourly wind-speed dynamics at nine automatic stations of the Brazilian National Institute of Meteorology in Paraíba, Northeast Brazil, over the common interval from 3 November 2017 to 17 November 2019. Missing records and values outside the [...] Read more.
This paper examines the multifractal organization of hourly wind-speed dynamics at nine automatic stations of the Brazilian National Institute of Meteorology in Paraíba, Northeast Brazil, over the common interval from 3 November 2017 to 17 November 2019. Missing records and values outside the inclusive 1.0–18.0 m/s analytical range are removed before station-level standardization, and multifractal detrended fluctuation analysis is applied to compacted retained-observation sequences. The stability-potential index (SPI) is defined as |α0 − 0.5|, where α0 is the singularity-spectrum peak and 0.5 is the uncorrelated benchmark. SPI therefore measures departure from random-like scaling and is interpreted as a temporal-organization indicator, not as a stand-alone measure of wind-power resource. Rolling windows of 720 retained observations, advanced by 168 observations, are assigned to seasons, El Niño, La Niña, neutral conditions, and tropical Atlantic-gradient regimes. The empirical design combines full-sample rankings, rolling spectra, two-way clustered ordinary least squares, Frisch–Newton bootstrap quantile regression, non-overlapping and coverage-threshold sensitivities, clock-span diagnostics, analytical-range and moment-order checks, 200 shuffled surrogates per station, and station-anchored inverse-distance-weighted maps. All full-sample α0 estimates exceed 0.5, with SPI ranging from 0.1108 in Cabaceiras to 0.3937 in Areia. El Niño is associated with lower rolling SPI in both baseline and controlled mean regressions and in the lower and median quantiles; this sign persists after excluding low-coverage Camaratuba. La Niña is not significant at the mean but is negative at the 0.90 quantile. No north-warm Atlantic-gradient windows occur in the common sample, while the south-warm gradient is positive only near the median quantile. Four of nine stations have original raw spectrum widths above the shuffled 97.5% bound. Across stations, exact two-sided Spearman tests show no supported monotonic association between coverage, wind-distribution descriptors, or altitude and α0, SPI, or W (n = 9; all p ≥ 0.194). The results document sample-specific spatial heterogeneity and climate-regime associations while showing that compacted-window duration, calm-wind screening, and the modest nine-station network require explicit sensitivity analysis and cautious generalization. Full article
(This article belongs to the Special Issue Multifractal and Time Series Analysis: Theory and Applications)
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