  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.
