Title: Structural Classification of Locally Stationary Time Series Based on Second-order Characteristics Show Chinese title

Title: 基于二阶特性的局部平稳时间序列的结构分类

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. Show Chinese abstract

Abstract: 时间序列分类对于众多科学和工程应用至关重要。 在本文中，我们提出了一种数值高效、实际竞争且理论严谨的分类方法，用于根据时域和二阶特征区分两类局部平稳时间序列。 我们的方法基于局部平稳时间序列的自回归逼近，结合了集成聚合和基于距离的阈值进行分类。 它对训练样本大小没有要求，并且当底层时间序列仅在二阶特征上略有差异时，被证明可以渐近地达到零误分类误差率。 通过密集的数值模拟和癫痫分类的真实脑电图数据分析，新方法被证明优于各种最先进的解决方案，包括基于小波、基于树、基于卷积的方法以及现代深度学习方法。