The paper derives some moment bounds for signatures of fractional Brownian motion and shows simulations where signature Lasso beats Lasso, but it never proves the claimed consistency.
Functional linear regression with truncated signatures.Journal of Multivariate Analysis, 192:105031, 2022
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Regularized Learning for Fractional Brownian Motion via Path Signatures
The paper derives some moment bounds for signatures of fractional Brownian motion and shows simulations where signature Lasso beats Lasso, but it never proves the claimed consistency.