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Functional linear regression with truncated signatures

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  • Fermanian, Adeline

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.

Suggested Citation

  • Fermanian, Adeline, 2022. "Functional linear regression with truncated signatures," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000483
    DOI: 10.1016/j.jmva.2022.105031
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    References listed on IDEAS

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    1. Terry Lyons, 2014. "Rough paths, Signatures and the modelling of functions on streams," Papers 1405.4537, arXiv.org.
    2. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    3. Brunel, Élodie & Mas, André & Roche, Angelina, 2016. "Non-asymptotic adaptive prediction in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 208-232.
    4. Li, Yehua & Hsing, Tailen, 2007. "On rates of convergence in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1782-1804, October.
    5. Imanol Perez Arribas & Cristopher Salvi & Lukasz Szpruch, 2020. "Sig-SDEs model for quantitative finance," Papers 2006.00218, arXiv.org, revised Jun 2020.
    6. Fermanian, Adeline, 2021. "Embedding and learning with signatures," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
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