The Signature Kernel

Darrick Lee () and Harald Oberhauser ()
Additional contact information
Darrick Lee: University of Edinburgh
Harald Oberhauser: University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter

A chapter in Signature Methods in Finance, 2026, pp 85-124 from Springer

Abstract: Abstract The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this chapter, we provide an introduction to the signature kernel by highlighting the analytic connection between the path signature and ordinary monomials. In particular, both the classical monomials and the path signature are universal and characteristic on compact domains: they can approximate functions, and characterize probability measures. However, issues arise in practice due to unbounded domains, computational complexity, and non-robustness. We show that these issues can be avoided via kernelization and robustification. To address the computational complexity, we provide an overview of the kernel trick: algorithms to efficiently compute the signature kernel which avoid direct computations of the signature. Furthermore, the signature kernel is highly flexible, and provides a canonical way to turn a given kernel on any domain into a kernel for sequences in that domain, while retaining its theoretical and computational properties. Finally, we survey applications and recent developments of the signature kernel.

Date: 2026
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-031-97239-3_3

Ordering information: This item can be ordered from
http://www.springer.com/9783031972393

DOI: 10.1007/978-3-031-97239-3_3

Access Statistics for this chapter

More chapters in Springer Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().