Nowcasting using regression on signatures

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.

An early version of this paper was the result of a collaboration with Silvia Lui, Will Malpass, Andrew Reeves, Craig Scott, Emma Small from the UK Office for National Statistics. An earlier implementation of our algorithm in Python is available at https://github.com/alan-turing-institute/Nowcasting_with_signatures