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Mathematics
Special Issues
Applications of Time Series Analysis
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Applications of Time Series Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 1373

Special Issue Editor

Dr. Esam Mahdi

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
Interests: time series analysis; spatio-temporal analysis; quantile regression; functional and structural MRI; interdisciplinary research

Special Issue Information

Dear Colleagues,

Time series analysis, with its diverse applications spanning from finance to climate science and from medicine to marketing, plays a pivotal role in uncovering patterns, forecasting trends, and driving decision-making processes in various domains. We aim to explore innovative dimensions within this domain, delving into theoretical frameworks, potential applications, and the seamless integration with machine learning, neural networks (NNs), as well as recent breakthroughs in multivariate and high-dimensional analyses across various domains.

Dr. Esam Mahdi
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • time series models
  • ARMA model
  • ARCH model
  • leverage
  • long memory
  • nonlinear time series
  • forecasting methods
  • portmanteau tests
  • autocorrelation function
  • time-varying parameters
  • machine learning models
  • neural networks
  • temporal data mining
  • cryptocurrency analysis

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Published Papers (2 papers)

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Research

25 pages, 1580 KiB  
Article
Online Monitoring of Structural Change Points Based on Ratio-Type Statistics
by Wenjie Li, Hao Jin and Minghua Wu
Mathematics 2025, 13(8), 1315; https://doi.org/10.3390/math13081315 - 17 Apr 2025
Viewed by 61
Abstract
For scenarios where the type of structural break in a time series is unknown, this paper proposes a modified ratio-type test statistic to enable effective online monitoring of structural breaks, while circumventing the estimation of long-term variance. Under specific assumptions, we rigorously derive [...] Read more.
For scenarios where the type of structural break in a time series is unknown, this paper proposes a modified ratio-type test statistic to enable effective online monitoring of structural breaks, while circumventing the estimation of long-term variance. Under specific assumptions, we rigorously derive the asymptotic distribution of the test statistic under the null hypothesis and establish its consistency under the alternative hypothesis. In cases where both variance and mean breaks coexist, we introduce a refined mixed-break monitoring procedure based on the consistent estimation of breakpoints. The proposed method first provides consistent estimations of the mean change points and variance change points separately; then, mean and variance removal are performed on original data; finally, the previously removed trend is added back. Compared to traditional monitoring methods, which have to use two test statistics, this method requires only one to simultaneously monitor both types of change points, resulting in a significantly simplified monitoring process. This approach effectively reduces mutual interference between the two types of breaks, thereby enhancing the power of the test. Extensive numerical simulations confirm that this method can accurately detect the presence of structural breaks and reliably identify their types. Finally, case studies are provided to demonstrate the efficacy and practical applicability of the proposed method. Full article
(This article belongs to the Special Issue Applications of Time Series Analysis)
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23 pages, 6097 KiB  
Article
Decomposition-Aware Framework for Probabilistic and Flexible Time Series Forecasting in Aerospace Electronic Systems
by Yuanhong Mao, Xin Hu, Yulang Xu, Yilin Zhang, Yunan Li, Zixiang Lu and Qiguang Miao
Mathematics 2025, 13(2), 262; https://doi.org/10.3390/math13020262 - 14 Jan 2025
Viewed by 669
Abstract
Degradation prediction for aerospace electronic systems plays a crucial role in maintenance work. This paper proposes a concise and efficient framework for multivariate time series forecasting that is capable of handling diverse sequence representations through a Channel-Independent (CI) strategy. This framework integrates a [...] Read more.
Degradation prediction for aerospace electronic systems plays a crucial role in maintenance work. This paper proposes a concise and efficient framework for multivariate time series forecasting that is capable of handling diverse sequence representations through a Channel-Independent (CI) strategy. This framework integrates a decomposition-aware layer to effectively separate and fuse global trends and local variations and a temporal attention module to capture temporal dependencies dynamically. This design enables the model to process multiple distinct sequences independently while maintaining the flexibility to learn shared patterns across channels. Additionally, the framework incorporates probabilistic distribution forecasting using likelihood functions, addressing the dynamic variations and uncertainty in time series data. The experimental results on multiple real-world datasets validate the framework’s effectiveness, demonstrating its robustness and adaptability in handling diverse sequences across various application scenarios. Full article
(This article belongs to the Special Issue Applications of Time Series Analysis)
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