Structural Classification of Locally Stationary Time Series Based on Second-order Characteristics

• URL: http://arxiv.org/abs/2507.04237v2
• Date: Thu, 10 Jul 2025 03:23:01 GMT
• Title: Structural Classification of Locally Stationary Time Series Based on Second-order Characteristics
• Authors: Chen Qian, Xiucai Ding, Lexin Li,
• Abstract summary: We present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series.<n>Our approach builds on the autoregressive approximation for locally stationary time series, combined with an ensemble aggregation and a distance-based threshold for classification.<n>It imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate.
• Score: 18.368110934638207
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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, combined with an ensemble aggregation and a distance-based threshold for classification. It 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 EEG data analysis for epilepsy classification.

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