PSA: regression to the mean/mean reversion is a statistical artifact, not a causal mechanism.
So mean regression says that children of tall parents are likely to be shorter than their parents, but it also says parents of tall children are likely to be shorter than their children.
Put in a different way, mean regression goes in both directions.
This is well-understood enough here in principle, but imo enough people get this wrong in practice that the PSA is worthwhile nonetheless.
Andres pointed out a sad corollary downstream of people’s misinterpretation of regression to the mean as indicating causality when there might be none. From Tversky & Kahneman (1982) via Andrew Gelman:
We normally reinforce others when their behavior is good and punish them when their behavior is bad. By regression alone, therefore, they are most likely to improve after being punished and most likely to deteriorate after being rewarded. Consequently, we are exposed to a lifetime schedule in which we are most often rewarded for punishing others, and punished for rewarding.
Note that in the context of trading/investing, the two terms are often used differently. There, “mean reversion” often means negative autocorrelation of returns, which can either be ~causal or driven by price level noise (which in turn is more like a “regression to the mean” idea). If you invest in a mean reversion strategy you tend to have an actual mechanism in mind though.
“Regression to the mean” is a less ambiguous term and generally means what you describe.
PSA: regression to the mean/mean reversion is a statistical artifact, not a causal mechanism.
So mean regression says that children of tall parents are likely to be shorter than their parents, but it also says parents of tall children are likely to be shorter than their children.
Put in a different way, mean regression goes in both directions.
This is well-understood enough here in principle, but imo enough people get this wrong in practice that the PSA is worthwhile nonetheless.
Nice post on this, with code: https://acastroaraujo.github.io/blog/posts/2022-01-01-regression-to-the-mean/index.html
Andres pointed out a sad corollary downstream of people’s misinterpretation of regression to the mean as indicating causality when there might be none. From Tversky & Kahneman (1982) via Andrew Gelman:
Note that in the context of trading/investing, the two terms are often used differently. There, “mean reversion” often means negative autocorrelation of returns, which can either be ~causal or driven by price level noise (which in turn is more like a “regression to the mean” idea). If you invest in a mean reversion strategy you tend to have an actual mechanism in mind though.
“Regression to the mean” is a less ambiguous term and generally means what you describe.