Mathematical Applications and Statistical Rigor (MASR)
type: channel
description: Mathematical Applications and Statistical Rigor (MASR) is an international, peer-reviewed scholarly journal devoted to advancing research at the intersection of deep mathematical theory, rigorous statistical methodology, and impactful real-world applications. MASR is founded on the conviction that mathematics and statistics achieve their highest value when they are not only theoretically sound but also decisively relevant to contemporary scientific, technological, and societal challenges. MASR is more than a publication venue; it is a global research community committed to building a durable bridge between abstraction and application. The journal serves as a meeting point for theorists, applied scientists, and interdisciplinary researchers who seek to translate mathematical and statistical innovation into robust, actionable solutions. Researchers are welcome to submit papers to MASR after preparing them according to the SIRG template and following the SIRG Publisher Ethics and Malpractice Statement. (MASR) follows the SIRG Publisher peer-review process in handling all submitted papers. By submitting their paper to MASR, authors confirm their agreement to SIRG Publisher terms, conditions, and publication ethics and Copyrights page. ISSN (Online): 3071-3811 Frequency: 6 Volumes Annually Editor-in-Chief: <img src="[binary]"> Prof. Dr. A.M. Elsawah Beijing Normal–Hong Kong Baptist University, CHINA. Email: amelsawah@bnbu.edu.cn Elsawah is an established scholar whose research bridges the two foundational pillars of quantitative science: the design of experiments and the analysis of complex data. His work focuses on developing novel methodologies for optimal experimental design in high-dimensional and complex systems, with applications spanning chemistry, engineering, biomedicine, and industrial processes. He is particularly recognized for integrating advanced statistical design with computational techniques for simulation-based experiments. Website: https://staff.bnbu.e…
publisher: Scientific Innovation Research Group (SIRG)
language: en
publication name: Mathematical Applications and Statistical Rigor (MASR)
issn: 3071-3811
copyright: Mathematical Applications and Statistical Rigor (MASR) content is published under a Creative Commons Attribution License (CCBY). This means that content is freely available to all readers upon publication, and content is published as soon as production is complete. Mathematical Applications and Statistical Rigor (MASR) seeks to publish the most influential papers that will significantly advance scientific understanding. Selected articles must present new and widely significant data, syntheses, or concepts. They should merit recognition by the wider scientific community and the general public through publication in a reputable scientific journal.
items: Spectral Analysis of Long Memory in Financial Volatility Dynamics: Evidence from the CAC 40 Stock Market Index
items: Benchmarking Low-Dimensional Projection Uniformity in Mixed Two- and Three-Level Designs
items: Lower Bounds of Unanchored Discrepancy for Mixed-Level U-Type Designs
items: Bi-OSW-MF-DFA: An Enhanced Multifractal Method for Gold and Silver Market Risk Assessment
items: Advances in Uniform Experimental Designs: A Decade Selective Review of Algorithmic Search and Deterministic Construction Methods

Spectral Analysis of Long Memory in Financial Volatility Dynamics: Evidence from the CAC 40 Stock Market Index
type: item
description: Long-memory processes are widely used in time series analysis to characterize persistent dependence structures over time. In financial markets, this phenomenon is particularly relevant for modeling volatility dynamics, which measure the variability and risk of asset returns. This study investigates the presence of long-memory behavior in financial volatility using a spectral analysis approach. While the persistence of volatility is a well-documented stylized fact in financial econometrics, traditional time-domain models such as ARCH, GARCH, and their extensions primarily capture short- and medium-term dependence in conditional variance, often failing to fully account for long-range dependence. This paper addresses this gap by employing a frequency-domain approach based on spectral analysis to detect long memory in volatility dynamics. The empirical study is conducted using daily data from the CAC 40 stock market index. The price series is transformed into logarithmic returns, with volatility proxied by squared returns. A comparative analysis between returns and squared returns reveals that returns exhibit weak autocorrelation, whereas squared returns display strong persistence—consistent with established stylized facts. To further examine this persistence, we perform spectral density analysis and a simulation study. The results reveal a significant concentration of spectral power at low frequencies, providing strong evidence of long-memory dynamics in volatility. These findings have important implications for volatility forecasting, risk management, and the specification of econometric models in financial applications.
subject: Original Research
  topic: section
subject: Methodological and Theoretical Advances
  topic: category
subject: Computational and Data-Intensive Science
  topic: category
subject: Interdisciplinary and Applied Sciences
  topic: category
subject: Spectral analysis
  topic: keywords
subject: Volatility modeling
  topic: keywords
subject: Long memory
  topic: keywords
subject: CAC 40 index
  topic: keywords
subject: Time Series Analysis
  topic: subjects
creator: Barkahoum Laala
rights: Copyright (c) 2026 Mathematical Applications and Statistical Rigor (MASR) https://creativecommons.org/licenses/by/4.0
date: 2026-03-10
publication date: 2026-03-10
starting page: 107
ending page: 126

Benchmarking Low-Dimensional Projection Uniformity in Mixed Two- and Three-Level Designs
type: item
description: The uniformity of low-dimensional projections is a fundamental consideration in the construction of experimental designs, particularly in screening experiments where the effect hierarchy principle dictates that lower-order effects dominate. This paper provides comprehensive benchmarks for assessing this uniformity in mixed two- and three-level balanced designs—a class of designs ubiquitous in industrial, pharmaceutical, and computer experiments. We investigate the projection-weighted symmetric discrepancy (PWSDisc) as a uniformity criterion that explicitly prioritizes low-dimensional projections. A closed-form analytical expression for PWSDisc is derived in terms of elementary coincidence counts, revealing its intrinsic combinatorial structure. Building on this representation, we establish a sharp, easily computable lower bound that serves as a gold standard for design optimality. A catalog of lower bounds for practical parameter combinations is provided, offering immediate benchmarks for practitioners. Furthermore, an updated threshold-accepting algorithm incorporating these bounds as a stopping rule is presented, enabling efficient construction of uniform mixed two- and three-level designs. The results fill a critical gap in the theory of projection-based uniformity and have direct applications in computer experiments, robust parameter design, and beyond.
subject: Original Research
  topic: section
subject: Methodological and Theoretical Advances
  topic: category
subject: Computational and Data-Intensive Science
  topic: category
subject: Interdisciplinary and Applied Sciences
  topic: category
subject: Uniformity
  topic: keywords
subject: Discrepancy
  topic: keywords
subject: Lower bound
  topic: keywords
subject: Projection
  topic: keywords
subject: Design and Analysis of Experiments
  topic: subjects
creator: S.M. Celem
creator: Fatih Tank
creator: Hong Qin
rights: Copyright (c) 2026 Mathematical Applications and Statistical Rigor (MASR) https://creativecommons.org/licenses/by/4.0/
date: 2026-03-05
publication date: 2026-03-05
starting page: 89
ending page: 106

Lower Bounds of Unanchored Discrepancy for Mixed-Level U-Type Designs
type: item
description: Uniform $U$-type designs are fundamental to modern experimental methodology, particularly in computer experiments and robust parameter design, owing to their ability to uniformly distribute points across the design space. This space-filling property confers resilience against model misspecification and provides an ideal foundation for nonparametric estimation. Despite their practical significance, constructing uniform designs that minimize a given discrepancy poses an inherently intractable combinatorial optimization problem. This challenge has motivated the pursuit of theoretical lower bounds, which serve as optimality benchmarks and termination criteria for heuristic search algorithms. Mixed two- and three-level designs are ubiquitous in practical experimental settings, including industrial experiments, clinical trials, and computer simulations. In this paper, we derive sharp, analytically tractable lower bounds for the unanchored discrepancy in mixed two- and three-level U-type designs. Leveraging Jensen's inequality and combinatorial optimization, we obtain closed-form expressions that are both computationally expedient and demonstrably tight. We further delineate necessary conditions under which these bounds are attainable and propose constructive methodologies for generating designs that achieve or approach these theoretical limits. The resulting benchmarks fill a critical gap in the theory of uniform designs and offer tangible utility in constructing optimal experimental plans for computer simulations and robust parameter studies.
subject: Original Research
  topic: section
subject: Methodological and Theoretical Advances
  topic: category
subject: Computational and Data-Intensive Science
  topic: category
subject: Uniform design
  topic: keywords
subject: Unanchored discrepancy
  topic: keywords
subject: Lower bound
  topic: keywords
subject: U-type design
  topic: keywords
subject: Threshold accepting
  topic: keywords
subject: Unanchored Discrepancy
  topic: subjects
subject: U-Type Designs
  topic: subjects
creator: S.M. Celem
creator: Hong Qin
rights: Copyright (c) 2026 Mathematical Applications and Statistical Rigor (MASR) https://creativecommons.org/licenses/by/4.0
date: 2026-03-01
publication date: 2026-03-01
starting page: 70
ending page: 88

Bi-OSW-MF-DFA: An Enhanced Multifractal Method for Gold and Silver Market Risk Assessment
type: item
description: Amid global economic uncertainty and inflationary pressures, precious metals have gained prominence as safe-haven assets, yet accurately quantifying their risk remains challenging due to the inherent limitations of existing fractal analysis methods. Conventional Multifractal Detrended Fluctuation Analysis (MF-DFA) suffers from boundary-induced artifacts and computational inefficiencies, which can distort risk measurements and obscure true market dynamics. To address this gap, we introduce an enhanced method—Binary Overlapped Sliding Window MF-DFA (Bi-OSW-MF-DFA)—that mitigates segmentation discontinuities and improves computational robustness through overlapping windows and binary series partitioning. Applied to spot gold and silver markets, our approach reveals that silver exhibits stronger multifractality and higher inherent risk than gold, with long-range temporal correlations identified as the primary driver of multifractal behavior. This study offers a refined analytical framework for market risk assessment and provides actionable insights for investors and portfolio managers navigating precious metals volatility.
subject: Original Research
  topic: section
subject: Computational and Data-Intensive Science
  topic: category
subject: Interdisciplinary and Applied Sciences
  topic: category
subject: MF-DFA
  topic: keywords
subject: Fractal theory
  topic: keywords
subject: Risk assessment
  topic: keywords
subject: Bi-OSW-MF-DFA
  topic: keywords
subject: Multifractal analysis
  topic: keywords
subject: Precious metals market
  topic: keywords
creator: Zhongjun Wang
creator: Mengye Sun
creator: A.M. Elsawah
rights: Copyright (c) 2026 Mathematical Applications and Statistical Rigor (MASR) https://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 57
ending page: 69

Advances in Uniform Experimental Designs: A Decade Selective Review of Algorithmic Search and Deterministic Construction Methods
type: item
description: This paper presents a comprehensive and selective review of the last decade's progress in the construction of uniform experimental designs. Confronting the growing complexity of modern experiments—characterized by high-dimensional factor spaces and constrained resources—recent research has produced promising methods tools for constructing efficient, cost-effective designs. The review is organized around three pivotal themes: (1) enhanced stochastic search algorithms, including adjusted threshold accepting and permutation-projection methods, for constructing (nearly) uniform minimum aberration designs, supported by benchmarks that reduce computational search; (2) frameworks for constructing uniform fold-over designs in two-stage sequential experimentations, enabling the breaking of aliasing structures across symmetric and asymmetric designs; and (3) deterministic construction algorithms—such as multiple doubling, tripling, and quadrupling, and their integration—for efficiently generating large-scale uniform designs with low, high, or mixed levels without exhaustive search. Collectively, these advances offer researchers a robust, computationally efficient, and theoretically coherent toolkit for designing experiments across scientific and industrial domains, representing a substantial leap beyond conventional methodologies. A critical discussion and comparative analysis of the reviewed methods are also provided, along with practical recommendations for implementation.
subject: Review Articles
  topic: section
subject: Methodological and Theoretical Advances
  topic: category
subject: Computational and Data-Intensive Science
  topic: category
creator: S.M. Celem
creator: Laala Barkahoum
creator: Gajendra Vishwakarma
creator: Hong Qin
rights: Copyright (c) 2026 Mathematical Applications and Statistical Rigor (MASR) https://creativecommons.org/licenses/by/4.0
date: 2026-01-20
publication date: 2026-01-20
starting page: 1
ending page: 56