Innovative Methods in Long Sequence Forecasting and Time Series Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 410

Special Issue Editors


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Guest Editor
School of Software, Beihang University, Beijing 100191, China
Interests: artificial intelligence and machine learning research with a focus on the application of time series forecasting; task decision making; AI safety; AI for science and other technologies in the industrial field and medical care

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Guest Editor
School of Computer Science and Engineering, Beihang University, Beijing 100191, China
Interests: data mining; artificial intelligence
School of Computer Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China
Interests: virtualization; resource management; distributed computing; graph data mining
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Special Issue Information

Dear Colleagues,

The increasing availability of temporal data across scientific and industrial domains has positioned time series analysis as a cornerstone of modern data-driven decision making. From decades-long financial market trends and climate modeling to continuous biomedical monitoring and industrial process control, the analysis of long sequential data persists as a critical research frontier. Emerging methodologies encompassing statistical models, machine learning architectures, deep neural networks, and signal processing techniques are reshaping our approach to long-scale temporal dependency modeling.

The design and analysis of innovative methods for time series analysis requires careful consideration of unique temporal characteristics such as non-stationarity, computational bottlenecks in ultra-long horizon forecasting and high-dimensionality, missing data imputation in multi-source systems, and uncertainty quantification in long sequence analysis and coupled spatial–temporal processes. Recent advances in state-space modeling, frequency domain analysis, nonlinear dynamics characterization, and hybrid approaches combining domain knowledge with data-driven techniques demonstrate the vibrant evolution of this field.

This Special Issue focuses on cutting-edge methodological developments that address fundamental challenges in temporal pattern recognition and forecasting, with an expanded scope to encompass spatial–temporal applications. We emphasize both theoretical rigor and practical implementation, requiring submissions to address reproducibility, computational efficiency, and empirical validation through real-world case studies. Submissions may range from pure methodological advances to applied research demonstrating transformative impact. Interdisciplinary studies bridging traditional time series analysis with emerging computational paradigms are especially encouraged.

We particularly welcome contributions that

  • Develop novel architectures for long sequence modeling and cross-scale temporal dependencies;
  • Establish theoretical guarantees for time series algorithms and spatial–temporal algorithms;
  • Design computationally efficient techniques for large-scale streaming data;
  • Create interpretable models balancing accuracy with explainability;
  • Propose robust methods for uncertainty-aware forecasting;
  • Create hybrid models balancing interpretable components with deep learning performance;
  • Demonstrate transformative applications in domains requiring long-context analysis (e.g., climate science, energy systems) or spatial–temporal reasoning (e.g., traffic networks, epidemiological spread).

Dr. Haoyi Zhou
Dr. Qingyun Sun
Dr. Bin Shi
Guest Editors

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Keywords

  • time series analysis
  • spatiotemporal forecasting
  • non-stationary process modeling
  • high-dimensionality embedding
  • interpretability–accuracy trade-off
  • frequency–time domain synthesis
  • long-term dependency modeling
  • cross-scale dependency learning
  • data-driven decision making
  • domain knowledge integration
  • interdisciplinary applications

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Published Papers (2 papers)

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Research

18 pages, 3717 KiB  
Article
A Hybrid LMD–ARIMA–Machine Learning Framework for Enhanced Forecasting of Financial Time Series: Evidence from the NASDAQ Composite Index
by Jawaria Nasir, Hasnain Iftikhar, Muhammad Aamir, Hasnain Iftikhar, Paulo Canas Rodrigues and Mohd Ziaur Rehman
Mathematics 2025, 13(15), 2389; https://doi.org/10.3390/math13152389 - 25 Jul 2025
Abstract
This study proposes a novel hybrid forecasting approach designed explicitly for long-horizon financial time series. It incorporates LMD (Local Mean Decomposition), SD (Signal Decomposition), and sophisticated machine learning methods. The framework for the NASDAQ Composite Index begins by decomposing the original time series [...] Read more.
This study proposes a novel hybrid forecasting approach designed explicitly for long-horizon financial time series. It incorporates LMD (Local Mean Decomposition), SD (Signal Decomposition), and sophisticated machine learning methods. The framework for the NASDAQ Composite Index begins by decomposing the original time series into stochastic and deterministic components using the LMD approach. This method effectively separates linear and nonlinear signal structures. The stochastic components are modeled using ARIMA to represent linear temporal dynamics, while the deterministic components are projected using cutting-edge machine learning methods, including XGBoost, Random Forest (RF), Artificial Neural Networks (ANNs), and Support Vector Machines (SVMs). This study employs various statistical metrics to evaluate the predictive ability across both short-term noise and long-term trends, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Directional Statistic (DS). Furthermore, the Diebold–Mariano test is used to determine the statistical significance of any forecast improvements. Empirical results demonstrate that the hybrid LMD–ARIMA–SD–XGBoost model consistently outperforms alternative configurations in terms of prediction accuracy and directional consistency. These findings demonstrate the advantages of integrating decomposition-based signal filtering with ensemble machine learning to improve the robustness and generalizability of long-term forecasting. This study presents a scalable and adaptive approach for modeling complex, nonlinear, and high-dimensional time series, thereby contributing to the enhancement of intelligent forecasting systems in the economic and financial sectors. As far as the authors are aware, this is the first study to combine XGBoost and LMD in a hybrid decomposition framework for forecasting long-horizon stock indexes. Full article
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24 pages, 3200 KiB  
Article
A Spatial–Temporal Time Series Decomposition for Improving Independent Channel Forecasting
by Yue Yu, Pavel Loskot, Wenbin Zhang, Qi Zhang and Yu Gao
Mathematics 2025, 13(14), 2221; https://doi.org/10.3390/math13142221 - 8 Jul 2025
Viewed by 259
Abstract
Forecasting multivariate time series is a pivotal task in controlling multi-sensor systems. The joint forecasting of all channels may be too complex, whereas forecasting the channels independently may cause important spatial inter-dependencies to be overlooked. In this paper, we improve the performance of [...] Read more.
Forecasting multivariate time series is a pivotal task in controlling multi-sensor systems. The joint forecasting of all channels may be too complex, whereas forecasting the channels independently may cause important spatial inter-dependencies to be overlooked. In this paper, we improve the performance of single-channel forecasting algorithms by designing an interpretable front-end that extracts the spatial–temporal components from the input multivariate time series. Specifically, the multivariate samples are first segmented into equal-sized matrix symbols. The symbols are decomposed into the frequency-separated Intrinsic Mode Functions (IMFs) using a 2D Empirical-Mode Decomposition (EMD). The IMF components in each channel are then forecasted independently using relatively simple univariate predictors (UPs) such as DLinear, FITS, and TCN. The symbol size is determined to maximize the temporal stationarity of the EMD residual trend using Bayesian optimization. In addition, since the overall performance is usually dominated by a few of the weakest predictors, it is shown that the forecasting accuracy can be further improved by reordering the corresponding channels to make more correlated channels more adjacent. However, channel reordering requires retraining the affected predictors. The main advantage of the proposed forecasting framework for multivariate time series is that it retains the interpretability and simplicity of single-channel forecasting methods while improving their accuracy by capturing information about the spatial-channel dependencies. This has been demonstrated numerically assuming a 64-channel EEG dataset. Full article
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