Cointegration

Cointegration is an econometric technique used for testing the relationship between non-stationary time series variables. If two or more series’ are individually integrated (minimum number of differences required to make a series stationary), but some linear combination of them has a lower order of integration, then the series’ are said to be cointegrated. For example, if X and Y are each integrated of order 1, and there exist coefficients a and b such that aX + bY is integrated of order 0, then X and Y are said to be cointegrated.

Example:

Consider a drunk man walking with his dog, both the drunkard and his dog take random walks. If the drunk periodically calls out his dog’s name, this will interrupt the dog’s aimless wandering and the dog will bark in response to his master. Both the drunk and the dog hear each other, the dog fears getting locked out if he strays far from his master whereas the master does not want to wake up in the middle of the night to the barking of his dog, this limits the distance between them from increasing indefinitely. If one were to follow the drunk or his dog, both will be roaming around in a seemingly aimless manner. The paths of the drunk and the dog are still non-stationary. Despite this, one might still observe that if the drunk’s location is known then it is unlikely that the dog would be very far away. The distance between the two paths is stationary and the paths of drunk and his dog are said to be cointegrated.