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Axioms
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Methods and Applications of Advanced Statistical Analysis, 3rd Edition
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Methods and Applications of Advanced Statistical Analysis, 3rd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 1721

Special Issue Editor

Dr. Tomas Ruzgas

E-Mail Website
Guest Editor
Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Interests: nonparametric statistics; application of functional analysis in statistics; hypothesis testing; multivariate analysis in social, environmental, medical sciences, etc.
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to exploring the latest advances in statistical analysis that are innovative in their theoretical, methodological, or applicability approach. Potential topics of interest for this Special Issue include, but are not limited to, survey sampling, nonparametric statistics, functional data analysis, Bayesian analysis, robust statistics, hypothesis testing, univariate and multivariate statistics, regression and analysis of variance, categorical data analysis, classification and clustering, mixed modelling, survival analysis, time series analysis, and their applications.

Dr. Tomas Ruzgas
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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms 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 2400 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

  • application of statistics
  • causal analysis
  • classification and clustering
  • data analysis
  • linear and nonlinear models
  • mixed modelling
  • nonparametric statistics
  • regression and analysis of variance
  • robust statistics
  • time series

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Related Special Issue

Published Papers (3 papers)

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Research

23 pages, 557 KB  
Article
A Multi-Stage Decomposition and Hybrid Statistical Framework for Time Series Forecasting
by Swera Zeb Abbasi, Mahmoud M. Abdelwahab, Imam Hussain, Moiz Qureshi, Moeeba Rind, Paulo Canas Rodrigues, Ijaz Hussain and Mohamed A. Abdelkawy
Axioms 2026, 15(4), 273; https://doi.org/10.3390/axioms15040273 - 9 Apr 2026
Viewed by 553
Abstract
Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limitations, this study proposes a novel three-stage hybrid statistical framework that systematically integrates [...] Read more.
Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limitations, this study proposes a novel three-stage hybrid statistical framework that systematically integrates multi-level signal decomposition with structured parametric modeling to enhance predictive accuracy. The proposed hybrid architectures—EMD–EEMD–ARIMA, EMD–EEMD–GMDH, and EMD–EEMD–ETS—employ a hierarchical decomposition–reconstruction strategy before forecasting. In the first stage, Empirical Mode Decomposition (EMD) decomposes the observed series into intrinsic mode functions (IMFs) and a residual component. In the second stage, Ensemble Empirical Mode Decomposition (EEMD) is applied to further refine the extracted components, mitigating mode mixing and improving signal separability. In the final stage, each reconstructed component is modeled using ARIMA, Exponential Smoothing State Space (ETS), and Group Method of Data Handling (GMDH) frameworks, and the individual forecasts are aggregated to obtain the final prediction. Empirical evaluation based on a recursive one-step-ahead forecasting scheme demonstrates consistent numerical improvements across all standard accuracy measures. In particular, the proposed EMD–EEMD–ARIMA model achieves the lowest forecasting error, reducing the root-mean-square error (RMSE) by approximately 6–7% relative to the best-performing single-stage model and by about 3–4% relative to the two-stage EMD-based hybrids. Similar improvements are observed in mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), indicating enhanced stability and robustness of the three-stage architecture. The results provide strong numerical evidence that multi-level decomposition combined with structured statistical modeling yields superior predictive performance for complex nonlinear and nonstationary time series. The proposed framework offers a mathematically coherent, computationally tractable, and systematically structured hybrid modeling strategy that effectively integrates noise-assisted decomposition with parametric and data-driven forecasting techniques. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 3rd Edition)
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23 pages, 831 KB  
Article
Periodic Asymmetric LogGARCH Stochastic Volatility Models: Structure and Application
by Omar Alzeley and Ahmed Ghezal
Axioms 2026, 15(3), 216; https://doi.org/10.3390/axioms15030216 - 13 Mar 2026
Cited by 1 | Viewed by 334
Abstract
This paper introduces a new class of periodic volatility models, namely, the Stochastic Volatility Periodic Logarithmic Asymmetric GARCH (PlogAG-SV) model. The proposed framework extends periodic logGARCH models by incorporating a stochastic volatility component combined with a distinctive threshold mechanism, thereby significantly enhancing their [...] Read more.
This paper introduces a new class of periodic volatility models, namely, the Stochastic Volatility Periodic Logarithmic Asymmetric GARCH (PlogAG-SV) model. The proposed framework extends periodic logGARCH models by incorporating a stochastic volatility component combined with a distinctive threshold mechanism, thereby significantly enhancing their ability to capture asymmetric and time-varying volatility dynamics. Sufficient conditions for strict stationarity, second-order stationarity, and the existence of higher-order moments are rigorously established, providing a comprehensive characterization of the model’s probabilistic properties. Parameter estimation is conducted via extensive Monte Carlo simulations, demonstrating the robustness and reliability of the proposed estimation procedure across a wide range of scenarios. Furthermore, the empirical relevance of the PlogAG-SV model is illustrated through an application to the Algerian dinar–euro exchange rate, highlighting its effectiveness in modeling real-world financial volatility. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 3rd Edition)
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15 pages, 994 KB  
Article
A Statistical Power Comparison from Multivariate and Univariate Latent Growth Models with Incomplete Data
by Kejin Lee
Axioms 2026, 15(3), 178; https://doi.org/10.3390/axioms15030178 - 28 Feb 2026
Viewed by 385
Abstract
Latent growth modeling (LGM) is widely used to examine group differences in developmental trajectories in educational research. With multiple outcomes of interest, a multiple-domain latent growth model (MDLGM) can be applied to account for associations among growth trajectories from the outcomes. While the [...] Read more.
Latent growth modeling (LGM) is widely used to examine group differences in developmental trajectories in educational research. With multiple outcomes of interest, a multiple-domain latent growth model (MDLGM) can be applied to account for associations among growth trajectories from the outcomes. While the MDLGM is conceived as a more powerful multivariate analysis technique when compared with univariate LGM, the examination of its methodological performance is very limited. Henceforth, this study compared the statistical power of the MDLGM and separate univariate LGMs via a simulation study with a two-group, two-domain design. Results indicated that the MDLGM and the set of LGMs showed largely comparable power, with a small advantage for the MDLGM under conditions of weak inter-domain correlation and small group differences and showed reduced power as missingness increased. These findings provide educational researchers with a guideline for model selection in longitudinal studies with multiple outcomes. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 3rd Edition)
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