Crosscutting Areas On Consistency of Signature Using Lasso

• 成果类型: Article
• 署名作者: Guo, Xin; Wang, Binnan; Zhang, Ruixun; Zhao, Chaoyi
• 署名单位: University of California System; University of California Berkeley; Peking University; Peking University; Peking University; Peking University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.1133
• 发表日期: 2025
• 关键词: hedging derivative securities; path; uniqueness; selection; EVOLUTION

摘要

Signatures are iterated path integrals of continuous and discrete-time processes, and their universal nonlinearity linearizes the problem of feature selection in time series data analysis. This paper studies the consistency of signature using Lasso regression, both theoretically and numerically. We establish conditions under which the Lasso regression is consistent both asymptotically and in finite sample. Furthermore, we show that the Lasso regression is more consistent with the Ito signature for time series and processes that are closer to the Brownian motion and with weaker interdimensional correlations, whereas it is more consistent with the Stratonovich signature for mean-reverting time series and processes. We demonstrate that signature can be applied to learn nonlinear functions and option prices with high accuracy, and the performance depends on properties of the underlying process and the choice of the signature.