Data science, machine learning & data visualization consultant and lecturer

Why is forecasting s-curves hard?

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Constance Crozier (@clcrozier on Twitter) shared an interesting simulation in which she tried to fit a sigmoid curve (s-curve) to predict a plateau in a time-series. The result was a very intuitive and convincing animation that shows how wrong her initial forecasts were.

The matter of fact is that this phenomenon is not new at all. My first post-University job involved fitting numerous pharmacodynamics models. We always had to keep in mind that if the available data does not account for at least 95% of the maximum effect, the model will be very much suboptimal. It took me a while, but I managed to find the reference for this phenomenon [here]. Maybe, when I have some time, I will repeat Constance Crozier’s analysis, and add confidence intervals to emphasize the point.

EDIT: I came the conclusion that the most important takaway message of this demonstration is the necessity of reporting uncertainty with any forecast, and how small the value of a forecast is without uncertainty estimations.

S-curves (or sigmoid functions) are commonly used to model the evolution of social or biological systems over time [1]. These functions start with exponential growth, then increase linearly, and finally level off (therefore end up looking like a wonky s). Many things that we think of as exponential functions will actually follow an s-curve (otherwise […]