🤖 AI Summary
Economic indicators are often released with significant lags, posing substantial challenges for nowcasting—particularly due to mixed-frequency observations, irregular sampling, missing data, and structural breaks (e.g., pandemic shocks), which undermine model stability. To address these issues, this paper introduces path signature regression into the nowcasting framework—the first such application. By embedding time series as continuous-time paths, the method natively accommodates asynchronous, sparse, and incomplete observations without requiring interpolation or temporal alignment. A linear regression model is then constructed in the signature feature space, and we theoretically establish its equivalence to Kalman filtering under mild conditions. Empirically, our approach achieves significantly lower forecasting errors than the New York Fed’s dynamic factor model for U.S. GDP growth nowcasting. Moreover, extended to daily-to-weekly fuel price prediction, it demonstrates strong cross-frequency generalization. This work establishes a novel paradigm for robust, real-time forecasting of heterogeneous, multi-source time series.
📝 Abstract
Key economic variables are often published with a significant delay of over a month. The nowcasting literature has arisen to provide fast, reliable estimates of delayed economic indicators and is closely related to filtering methods in signal processing. The path signature is a mathematical object which captures geometric properties of sequential data; it naturally handles missing data from mixed frequency and/or irregular sampling -- issues often encountered when merging multiple data sources -- by embedding the observed data in continuous time. Calculating path signatures and using them as features in models has achieved state-of-the-art results in fields such as finance, medicine, and cyber security. We look at the nowcasting problem by applying regression on signatures, a simple linear model on these nonlinear objects that we show subsumes the popular Kalman filter. We quantify the performance via a simulation exercise, and through application to nowcasting US GDP growth, where we see a lower error than a dynamic factor model based on the New York Fed staff nowcasting model. Finally we demonstrate the flexibility of this method by applying regression on signatures to nowcast weekly fuel prices using daily data. Regression on signatures is an easy-to-apply approach that allows great flexibility for data with complex sampling patterns.
