Nowcasting with Signature Methods

Abstract

Nowcasting refers to the “forecast” of the current (“now”) state of the econ- omy. This is necessary as key economic variables are often published with a significant delay of over a month. The nowcasting literature has arisen to address the need to have fast, reliable estimates of delayed economic indica- tors. 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 merg- ing multiple data sources – by embedding the observed data in continuous time. Calculating path signatures and using them as features in models have achieved state-of-the-art results in other 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 application to US GDP growth, where in the latter we demonstrate no loss of performance compared with the dynamic factor model. By embedding discrete information in continuous time, this approach allows greater flexibility for future applications on data with complex sam- pling patterns.