Cointegration and Long-Horizon Forecasting (2025)

Cointegration is an interesting measure that was introduced to deal with the problem of spurious correlation in time series regression analysis[1]. As I understand it, if you have a bunch of time series that are individually "integrated of order d" (meaning they need d differences to be stationary) but there is some linear combination of them that is integrated of order less than d then they are said to be cointegrated. Intuitively you could say that means they make more sense taken together than they do individually.

The analogy that I remember reading once is say your time series are people walking down the street. If they are walking next to each other, they are correlated. That is, you know they are directionally travelling together but you are unsure of any causal relationship. If they are walking hand-in-hand on the other hand, they are cointegrated.

[1] https://en.wikipedia.org/wiki/Cointegration

This paper is from 1997 ...