On Consistency of Signature Using Lasso

The signature transform is a powerful tool for feature extraction in time series analysis, yet its statistical properties remain underexplored. In their paper in Operations Research, Guo et al. examine the consistency of signature when used with Lasso regression. The study establishes conditions under which Lasso achieves consistent feature selection, both asymptotically and in finite samples. A key finding is that the Itô signature performs better for processes resembling Brownian motion, whereas the Stratonovich signature is more effective for mean-reverting processes. The authors further demonstrate the practical relevance of their results by applying signature-based Lasso regression to option pricing, highlighting its potential in financial modeling. These insights provide a crucial theoretical foundation for improving predictive performance across various domains, including operations research and machine learning.