Signature Transform Application in Time Series Analysis: An Introduction to Classification and Reconstruction Problems

Abstract

The goal of this paper is to analyze comprehensively how the Signature Transform can be used for the classification of time series. Data preprocessed with the signature transform can theoretically be classified using only linear models, which represents an advantage over more traditional algorithms. Unlike existing papers, our goal is to offer a self-contained, compact work that is accessible to audiences with a more limited mathematical background. The exposition is deliberately soft, and the experiments are short and clear, aiming to provide all the details necessary for full reproducibility. In our illustrative example, we work with sine waves (signals) of only two different possible frequencies, carefully pointing out every step of the methodology. Remarks on how to visualize time series in a simple two dimensional (2D) plane are included, as visualization represents an important step in developing an intuitive understanding of the problem. Finally, we discuss an alternative application in signal reconstruction, with the aim of building an encoder/decoder system. Important limitations arise in this final section, which nevertheless open a way to improve a clear and intuitive interpretation of such a transform.