[Paper Review] Nowcasting using regression on signatures

Samuel N. Cohen, Giulia Mantoan+4 more|arXiv (Cornell University)|May 17, 2023

Complex Systems and Time Series AnalysisEconomics, Econometrics and Finance3 citations

TL;DR

This paper introduces regression on signatures, a novel nowcasting method that uses path signatures—nonlinear features derived from continuous-time time series—to model economic indicators with mixed-frequency, irregular, or missing data. The approach achieves state-of-the-art performance, outperforming dynamic factor models in US GDP nowcasting and enabling flexible, interpretable, and easy-to-implement forecasting with minimal modeling complexity.

ABSTRACT

We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observations in continuous time, they naturally handle mixed frequencies and missing data. We prove theoretically, and with simulations, that regression on signatures subsumes the linear Kalman filter and retains desirable consistency properties. Nowcasting with signatures is more robust to disruptions in data series than previous methods, making it useful in stressed times (for example, during COVID-19). This approach is performant in nowcasting US GDP growth, and in nowcasting UK unemployment.

Motivation & Objective

• To address the challenge of delayed economic indicators by developing a flexible, robust nowcasting method that handles mixed-frequency and irregularly sampled data.
• To improve upon existing nowcasting models by leveraging path signatures as features that naturally encode temporal dynamics and missing data patterns.
• To provide a simple, interpretable, and extensible framework that subsumes traditional methods like the Kalman filter while enabling nonlinear relationships without complex modeling.
• To demonstrate the method’s effectiveness through real-world applications in US GDP growth and weekly fuel price nowcasting.
• To promote reproducibility and adoption by releasing a public Python package, SigNow, and open-source code.

Proposed method

• The method computes path signatures from continuous-time time series data, which encode geometric and temporal properties of sequential observations, enabling robust handling of missing or irregularly sampled data.
• It applies standard linear regression on the signature features, reducing complex time series modeling to a two-step process: signature computation and linear fitting.
• The approach uses a truncated signature expansion up to a specified level (e.g., level 3 or 4), with all linear terms retained to preserve predictive power.
• Signature terms are standardized, and the target variable is used as a multiplier in signature computation to improve predictive alignment.
• Missing data is handled via forward fill or rectilinear interpolation, depending on the data type and application.
• Regularization via elastic net (specifically ridge, α=1.0 or 2.0) is applied to prevent overfitting, with hyperparameters tuned via cross-validation.

Experimental results

Research questions

• RQ1 Can path signatures serve as effective, nonlinear features for nowcasting economic indicators with mixed-frequency and irregularly sampled data?
• RQ2 How does regression on signatures compare in performance to established dynamic factor models in US GDP nowcasting?
• RQ3 To what extent can the method handle missing data and irregular sampling without requiring data imputation or complex preprocessing?
• RQ4 Can the method be flexibly applied to diverse nowcasting tasks, such as forecasting weekly fuel prices from daily data?
• RQ5 Does the signature-based approach maintain interpretability while outperforming black-box machine learning models?

Key findings

• Regression on signatures achieved lower prediction error than the New York Fed dynamic factor model in nowcasting US GDP growth, demonstrating superior performance on real-world data.
• The method successfully handled mixed-frequency and irregularly sampled data without data imputation, relying on continuous-time signature computation to embed missing observations naturally.
• In the fuel price nowcasting task, the model achieved strong predictive accuracy using only 17 days of daily data and a signature level of 4, with a regularization strength of α=0.5.
• The approach outperformed traditional methods in terms of both accuracy and robustness, particularly in scenarios with incomplete or unevenly spaced observations.
• The use of path signatures enabled the model to capture complex temporal dependencies without requiring nonlinear models or extensive hyperparameter tuning.
• The open-source SigNow package and reproducible codebase enable broad adoption and extension of the method to other nowcasting applications.