# On Consistency of Signature Using Lasso

arXiv: https://arxiv.org/abs/2305.10413 · HTML: https://mlsanity.com/paper/2305.10413/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2023.

## Built on by (most cited first, 5 of 5)

- [Universal approximation with signatures of non-geometric rough paths](https://mlsanity.com/paper/2602.05898/) (2026)
- [Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting](https://mlsanity.com/paper/2510.12337/) (2025)
- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)
- [Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures](https://mlsanity.com/paper/2606.15332/) (2026)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)

## Abstract (arXiv)

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 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.