Sig-Splines: universal approximation and convex calibration of time series generative models

ArXiv ID: 2307.09767 “View on arXiv”

Authors: Unknown

Abstract

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a seamless substitution for traditional neural networks. This approach enables us to achieve not only the universality property inherent in neural networks but also introduces convexity in the model’s parameters.

Keywords: generative model, neural spline flows, signature transform, time series, multivariate data, General Financial Data Modeling

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper relies on dense advanced mathematics like rough path theory, signature transforms, and convex optimization proofs, but the excerpt shows no implementation details, backtests, or data; it focuses on theoretical universality and convexity rather than empirical validation.

  flowchart TD
    A["Research Goal<br>Universal generative model for<br>multivariate time series with<br>convex parameter calibration"] --> B{"Methodology"}
    B --> C["Data Input<br>General Financial Time Series"]
    B --> D["Sig-Splines Architecture<br>Linear Transformation +<br>Signature Transform"]
    C --> E["Computational Process<br>Kernel Density Estimation<br>via Neural Spline Flows"]
    D --> E
    E --> F["Key Findings/Outcomes"]
    F --> G["Universal Approximation<br>Guarantees"]
    F --> H["Convex Calibration<br>Properties"]