Time Series Modeling of COVID-19 Paths

Check out the refreshing new paper by Andrew Harvey and Paul Kattuman "Time series models based on growth curves with applications to forecasting coronavirus", pp. 126-156 here.

For non-causal forecasting, reduced-form approaches like those of Harvey-Kattuman are almost always the way to go, from traditional time series modeling to more recent extensions in machine learning. To paraphrase a long-ago No Hesitations post:  We generally don't need deep structural understanding to succeed at forecasting, which is wonderful, because we typically don't have deep structural understanding. (Admit it.) 

Forecasting COVID progression (cases, deaths, etc.) is a fine example. The leading structural ("SIR") model is a toy model, an intentionally stripped-down abstraction of a much more complex reality.  There's nothing wrong with that -- that's what all structural models are, and good structural models can yield invaluable insights. But good forecasting requires capturing the complex reality more fully, with its model uncertainty, measurement uncertainty, parameter uncertainty, innovation uncertainty, structural change uncertainty, etc. That's where reduced-form approaches shine.

On the other hand, because structural models can in principle illuminate the causal mechanisms that underlie reduced-form correlations, they may help with analysis of conterfactuals. That is, structural models may facilitate causal forecasting in addition to non-causal forecasting.

Of course it doesn't have to be an either/or choice.  One can attempt to blend the structural and reduced-form approaches, hoping to achieve the best of both worlds. To that end, see the also-refreshing new paper by Andrew Atkeson et al., "Estimating and forecasting disease scenarios for COVID-19 with an SIR model", here.