Recurrence and Stationarity

The recurrent nature of the past

We could say that a good forecast for tomorrow’s weather would be today’s, plus or minus a couple of raindrops. This is to say that the weather is a system with memory: The past has an impact on the present. Or, to put it in yet a different way, the past is recurrent.

To say that today is determined by tomorrow is certainly very intuitive. In fact, it is a view that permeates statistics into fields as diverse as history, biology, or finance. Still, we must not forget that, in many cases, this is a reasonable assumption and motivated by our perspective on the subject matter. But sometimes, it won’t necessarily be true. Nassim N. Taleb talks about this in his book, The Black Swan. Imagine a turkey that is fed every day by a butcher. The turkey will think that the normal course of life is to get food for no particular reason. If it were to predict the future based on the past, the turkey would say that food would keep coming. However, we know this is just an illusion. At some point, say Thanksgiving, the turkey will become someone’s dinner.