On Consistency of Signature Using Lasso

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...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Guo, Xin, Wang, Binnan, Zhang, Ruixun, Zhao, Chaoyi
Format: Article
Language:English
Subjects:
Brownian motion
Consistency
Integrals
Machine learning
Random walk
Regression
Signatures
Statistical analysis
Statistical inference
Stochastic models
Time series
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Summary: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 inter-dimensional correlations, while 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.
ISSN:2331-8422