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When correlation is more than just that: Bird is a word
“The future will be the child of the past and the present, even if a rebellious child.“ This quote belongs to George Crumb—an American composer of classical music. I don’t listen to classical music, and I had not heard of George Crumb until when I searched for a quote by Ilia Chavchavadze—a Georgian public figure of the late 19th and early 20th centuries—who said: “The present born from the past is a parent of the future.“
They were not experts in forecasting or in time series econometrics. But in their quotes, they both described rather eloquently the concept of forecasting: we are able to make an educated guess about the future because we can observe and take lessons from the past. Which is the very essence of time series econometrics.
In the wake of the credibility revolution, time series analysis took the back seat or, at least, did not keep pace with causal inference, which has emerged as the dominant force in econometric analysis. But even before that, jokes were made at the expense of time series econometrics.
Fair enough. Time series analysis, and especially forecasting, has never been about causality. At least not in the non-Granger sense. But so long as we are keen on predicting the future, a mere correlation, which may not be causally identified, might as well suffice.
Here, I don't mean any correlation. Consider birds' behavior in the wake of a storm. As the adage goes: "Hawks flying high means a clear sky. When they fly low, prepare for a blow." For ages, people used to rely on birds’ behavior to predict upcoming changes to the weather.
As it turns out, birds are sensitive to changes in air pressure. They are 'nature's barometers' of the sort. So they start flying low when air pressure drops, which in turn leads to the formation of a storm. We know it now, but our predecessors did not know it back when the barometer was yet to be invented.
But birds did not cause storms, changes in pressure—and other related stuff that goes on in the atmosphere—did. Both the birds' behavior and the storm are the outcome of that same cause, air pressure (P). And as it happens, one outcome, birds' behavior (B), precedes the other outcome, the storm (S). Here is a graphical illustration of this:
The time subscripts here are arbitrary. They serve as clarifiers of the chronological order of events. The solid lines indicate causality. The dashed line indicates correlation (without causality). Thus, even if just a correlation, birds’ behavior served as a ‘useful’ predictor of the storm. That’s all, our predecessors could ask for.
Replication material is available here.
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