Generalized Signature Method for Multivariate Time Series: A Data-Driven Framework for Feature Extraction

The signature method, rooted in controlled differential equation theory, offers a robust approach to feature extraction from multimodal sequential data, widely applicable in data science. This study presents a generalized signature framework that unifies existing variations, categorizing them into augmentations, windows, transforms, and rescalings. By integrating these methods, we develop new combinations to optimize feature extraction for multivariate time series analysis. An extensive empirical evaluation on 26 datasets identifies which configurations yield the best predictive performance, leading to a canonical pipeline for the generalized signature method. This optimized approach achieves state-of-the-art accuracy on benchmark problems in multivariate time series classification, offering a powerful tool for data scientists working with complex sequential data.