Understanding the Commodity Futures Term Structure Through Signatures

ArXiv ID: 2503.00603 “View on arXiv”

Authors: Unknown

Abstract

Signature methods have been widely and effectively used as a tool for feature extraction in statistical learning methods, notably in mathematical finance. They lack, however, interpretability: in the general case, it is unclear why signatures actually work. The present article aims to address this issue directly, by introducing and developing the concept of signature perturbations. In particular, we construct a regular perturbation of the signature of the term structure of log prices for various commodities, in terms of the convenience yield. Our perturbation expansion and rigorous convergence estimates help explain the success of signature-based classification of commodities markets according to their term structure, with the volatility of the convenience yield as the major discriminant.

Keywords: Path Signatures, Commodity Markets, Term Structure, Convenience Yield, Interpretability

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring advanced stochastic calculus, perturbation expansions of signatures, and rigorous convergence estimates, which drives a high math score. However, it presents no backtests, code, or statistical implementation details; it is fundamentally a theoretical framework for interpreting an existing classifier, making it low on empirical rigor.

  flowchart TD
    A["Research Goal: Explain why<br>signatures work for<br>commodity term structure classification"] --> B["Methodology: Signature Perturbations<br>Regular perturbation of signatures<br>in terms of convenience yield"]
    B --> C["Data & Inputs<br>Log prices of various commodities<br>Derived convenience yield"]
    C --> D["Computational Process<br>Construct perturbation expansion<br>Apply rigorous convergence estimates"]
    D --> E["Key Finding 1<br>Volatility of convenience yield<br>is the major discriminant"]
    D --> F["Key Finding 2<br>Perturbation explains success of<br>signature-based classification"]
    E --> G["Outcome: Enhanced interpretability<br>of signature methods<br>in financial markets"]
    F --> G