Innovative Methods in Long Sequence Forecasting and Time Series Analysis

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

Manuscript Submission Information

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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.

• 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