  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.
