Tropical time series, iterated-sums signatures and quasisymmetric functions

Abstract

Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of (real-valued) time series that are not easily available using existing signature-type objects. We demonstrate how the signature extracts chronological aspects of a time series, and that its calculation is possible in linear time. We identify quasisymmetric expressions over semirings as the appropriate framework for iterated-sums signatures over semiring-valued time series.

fix notational errors, clarify certain proofs

References in corpus (2)

• Tensor categorical foundations of algebraic geometry
• Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections

Cited by in corpus (3)

• Generalized iterated-sums signatures
• On the signature of an image
• Decomposing Tensor Spaces via Path Signatures