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

TL;DR

This paper introduces a new classification method for locally stationary time series based on second-order characteristics, combining autoregressive approximation with ensemble and thresholding, achieving high accuracy and outperforming existing methods.

Contribution

The paper proposes a novel, theoretically rigorous classification approach that requires no training sample size and asymptotically achieves zero error for mildly differing second-order time series.

Findings

Outperforms wavelet, tree, convolution, and deep learning methods in simulations.

Achieves zero misclassification error asymptotically under mild differences.

Demonstrated effectiveness on EEG epilepsy data.

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.