Sigmoids behaving badly: why they usually cannot predict the future as well as they seem to promise

Abstract

Sigmoids (AKA s-curves or logistic curves) are commonly used in a diverse spectrum of disciplines as models for time-varying phenomena showing initial acceleration followed by slowing: technology diffusion, cumulative cases of an epidemic, population growth towards a carrying capacity, etc. Existing work demonstrates that retrospective fit of data is often impressive. We show that in time series data, the future fit tends to be poor unless the data covers the entire range from before to after the inflection point. We discuss the theoretical reasons for this: the growth data provides little information about the damping term (and vice-versa). As a consequence, forecasting with sigmoids tends to be very unreliable. We suggest some practical approaches to improving the viability of forecasting sigmoid models.