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[2509.23597] Characteristic Root Analysis and Regularization for Linear Time Series Forecasting
Summary
This paper explores the effectiveness of linear models for time series forecasting, focusing on characteristic roots and their impact on model performance in both noise-free and noisy environments.
Why It Matters
Time series forecasting is crucial across various fields, and understanding the dynamics of linear models can lead to more robust and interpretable forecasting methods. This research highlights the importance of characteristic roots and offers strategies to enhance model performance, which can significantly benefit practitioners in data science and machine learning.
Key Takeaways
- Characteristic roots play a vital role in the long-term behavior of linear time series models.
- Noise in data can lead to spurious roots, necessitating larger training datasets for effective learning.
- Two proposed strategies, Reduced-Rank Regression and Root Purge, improve model robustness against noise.
Computer Science > Machine Learning arXiv:2509.23597 (cs) [Submitted on 28 Sep 2025 (v1), last revised 25 Feb 2026 (this version, v3)] Title:Characteristic Root Analysis and Regularization for Linear Time Series Forecasting Authors:Zheng Wang, Kaixuan Zhang, Wanfang Chen, Xiaonan Lu, Longyuan Li, Tobias Schlagenhauf View a PDF of the paper titled Characteristic Root Analysis and Regularization for Linear Time Series Forecasting, by Zheng Wang and 5 other authors View PDF HTML (experimental) Abstract:Time series forecasting remains a critical challenge across numerous domains, yet the effectiveness of complex models often varies unpredictably across datasets. Recent studies highlight the surprising competitiveness of simple linear models, suggesting that their robustness and interpretability warrant deeper theoretical investigation. This paper presents a systematic study of linear models for time series forecasting, with a focus on the role of characteristic roots in temporal dynamics. We begin by analyzing the noise-free setting, where we show that characteristic roots govern long-term behavior and explain how design choices such as instance normalization and channel independence affect model capabilities. We then extend our analysis to the noisy regime, revealing that models tend to produce spurious roots. This leads to the identification of a key data-scaling property: mitigating the influence of noise requires disproportionately large training data, highlighting the nee...
