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Transportation Marketplace Rate Forecast Using Signature Transform

Haotian Gu, Xin Guo, Timothy L. Jacobs, Philip Kaminsky, Xinyu Li

TL;DR

The paper tackles forecasting freight marketplace rates, a nonstationary problem with regime shifts, by introducing a signature-transform–based forecasting framework. It leverages the universal nonlinearity of the signature transform to linearize complex temporal dependencies and uses a signature kernel to measure time-series similarity, enabling adaptive weighting in linear models. The authors develop an adaptive two-step LASSO procedure that uses signature features and kernel-based weights to capture seasonality and regime switching, achieving large improvements in accuracy and interpretability. Deployed at Amazon, the approach yields more than a $5\times$ improvement in forecast accuracy and about $50$ million in annual savings, robust to major disruptions such as the COVID-19 pandemic and geopolitical shocks. Overall, the work provides a practical, theoretically grounded forecasting framework for high-variance, factor-rich time series in transportation markets with real-time deployment benefits.

Abstract

Freight transportation marketplace rates are typically challenging to forecast accurately. In this work, we have developed a novel statistical technique based on signature transforms and have built a predictive and adaptive model to forecast these marketplace rates. Our technique is based on two key elements of the signature transform: one being its universal nonlinearity property, which linearizes the feature space and hence translates the forecasting problem into linear regression, and the other being the signature kernel, which allows for comparing computationally efficiently similarities between time series data. Combined, it allows for efficient feature generation and precise identification of seasonality and regime switching in the forecasting process. An algorithm based on our technique has been deployed by Amazon trucking operations, with far superior forecast accuracy and better interpretability versus commercially available industry models, even during the COVID-19 pandemic and the Ukraine conflict. Furthermore, our technique is able to capture the influence of business cycles and the heterogeneity of the marketplace, improving prediction accuracy by more than fivefold, with an estimated annualized saving of \$50MM.

Transportation Marketplace Rate Forecast Using Signature Transform

TL;DR

The paper tackles forecasting freight marketplace rates, a nonstationary problem with regime shifts, by introducing a signature-transform–based forecasting framework. It leverages the universal nonlinearity of the signature transform to linearize complex temporal dependencies and uses a signature kernel to measure time-series similarity, enabling adaptive weighting in linear models. The authors develop an adaptive two-step LASSO procedure that uses signature features and kernel-based weights to capture seasonality and regime switching, achieving large improvements in accuracy and interpretability. Deployed at Amazon, the approach yields more than a improvement in forecast accuracy and about million in annual savings, robust to major disruptions such as the COVID-19 pandemic and geopolitical shocks. Overall, the work provides a practical, theoretically grounded forecasting framework for high-variance, factor-rich time series in transportation markets with real-time deployment benefits.

Abstract

Freight transportation marketplace rates are typically challenging to forecast accurately. In this work, we have developed a novel statistical technique based on signature transforms and have built a predictive and adaptive model to forecast these marketplace rates. Our technique is based on two key elements of the signature transform: one being its universal nonlinearity property, which linearizes the feature space and hence translates the forecasting problem into linear regression, and the other being the signature kernel, which allows for comparing computationally efficiently similarities between time series data. Combined, it allows for efficient feature generation and precise identification of seasonality and regime switching in the forecasting process. An algorithm based on our technique has been deployed by Amazon trucking operations, with far superior forecast accuracy and better interpretability versus commercially available industry models, even during the COVID-19 pandemic and the Ukraine conflict. Furthermore, our technique is able to capture the influence of business cycles and the heterogeneity of the marketplace, improving prediction accuracy by more than fivefold, with an estimated annualized saving of \$50MM.
Paper Structure (31 sections, 4 theorems, 27 equations, 1 figure, 4 tables, 2 algorithms)

This paper contains 31 sections, 4 theorems, 27 equations, 1 figure, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Overview.
  3. The key challenges in time series forecasting.
  4. Machine learning models and signature transform.
  5. Our work.
  6. Implementation and real-time performance.
  7. Technical Background
  8. Signatures of Continuous Paths
  9. Notation
  10. Signature of Discrete Data
  11. Key Properties of Signature
  12. Computation of Signature Transform
  13. Improving computational efficiency.
  14. A Generic Framework for Linear Statistical Models with Signature Transform
  15. Forecasting Problem
  16. ...and 16 more sections

Key Result

Theorem 1

Let $X:[a, b] \rightarrow \mathbb{R}^{d}$ be a continuous piecewise smooth path. Then $\operatorname{Sig}(\widehat{X})$ uniquely determines $X$ up to translation.

Figures (1)

  • Figure 1: Flowchart illustrating the application of Algorithm \ref{['algo:lasso_sig']} to transportation marketplace rate forecast

Theorems & Definitions (11)

  • Definition 1
  • Remark 1
  • Example 1
  • Example 2
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1: Uniqueness hambly2010uniqueness
  • Theorem 2: Universal nonlinearity arribas2018derivatives
  • Theorem 3: Factorial decay lyons2007differential
  • ...and 1 more