On Consistency of Signature Using Lasso

Xin Guo (), Binnan Wang (), Ruixun Zhang () and Chaoyi Zhao ()
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Xin Guo: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720
Binnan Wang: School of Mathematical Sciences, Peking University, Beijing 100871, China
Ruixun Zhang: School of Mathematical Sciences, Peking University, Beijing 100871, China; and Center for Statistical Science, Peking University, Beijing 100871, China; and Laboratory for Mathematical Economics and Quantitative Finance, Peking University, Beijing 100871, China; and National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing 100871, China
Chaoyi Zhao: Sloan School of Management and Laboratory for Financial Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142

Operations Research, 2025, vol. 73, issue 5, 2530-2549

Abstract: 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 Itô 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.

Keywords: Machine; Learning; and; Data; Science; signature transform; Lasso; consistency; correlation structure; machine learning; option pricing (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:5:p:2530-2549

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