Functional linear regression with truncated signatures

Adeline Fermanian

Journal of Multivariate Analysis, 2022, vol. 192, issue C

Abstract: We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a function as an infinite series of its iterated integrals. The signature depends crucially on a truncation parameter for which an estimator is provided, together with theoretical guarantees. An empirical study on both simulated and real-world datasets shows that the resulting methodology is competitive with traditional functional linear models, in particular when the functional covariates take their values in a high dimensional space.

Keywords: Functional data analysis; Linear regression; Signatures (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2022.105031

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