Structural classification of locally stationary time series based on second-order characteristics

• 成果类型: Article; Early Access
• 署名作者: Qian, Chen; Ding, Xiucai; Li, Lexin
• 署名单位: University of California System; University of California Davis; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag083
• 发表日期: 2026-06-23
• 关键词: autocovariance function; autoregressive approximation; electroencephalogram; Locally Stationary Time Series; time series classification; DISCRIMINANT-ANALYSIS; Matrix Estimation; covariance; inference; features

摘要

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate asymptotically when the underlying time series differ only mildly in their second-order characteristics. The new method is demonstrated to outperform a variety of state-of-the-art solutions, including wavelet-based, tree-based, convolution-based methods, as well as modern deep learning methods, through intensive numerical simulations and a real electroencephalography data analysis for epilepsy classification.