Application of the signature method in time series and financial data streams

Abstract

This thesis focuses into the signature method’s role as a robust tool in data science, specifically within the realms of time series analysis and financial data streams. Originating from rough paths theory, the signature method offers a comprehensive representation of sequential data, effectively capturing intricate patterns and dependencies crucial for advanced modeling and predictive analytics. Establishing a solid theoretical foundation, this thesis explores how the signature method transforms raw time series data into structured representations that preserve essential dynamic information. Through theoretical insights and practical illustrations, the thesis demonstrates the method’s efficacy in enhancing model classification, temporal segmentation, and understanding complex model structures.