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On Consistency of Signature Using Lasso

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xin Guo & Binnan Wang & Ruixun Zhang & Chaoyi Zhao, 2025. "On Consistency of Signature Using Lasso," Operations Research, INFORMS, vol. 73(5), pages 2530-2549, September.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:5:p:2530-2549
    DOI: 10.1287/opre.2024.1133
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