---
tag: V1S1223G5E
kind: concept
name: Cointegration
msc: [62M10, 91B84, 62P20]
sources:
  - url: https://en.wikipedia.org/wiki/Cointegration
same_as:
  wikidata: Q1751675
  wikipedia: Cointegration
---

## Summary

Several non-stationary time series are cointegrated when some linear combination of them is stationary.
The series then wander, but they wander together, held by a long-run equilibrium relation.
Clive Granger introduced the idea, and Robert Engle and Granger developed its theory and tests in a 1987 paper.
Cointegration is central in the econometrics of prices, interest rates and other economic series.

## Explanations

### L1 human

Picture a person walking a dog on a long leash through a park.
Each path wanders unpredictably, but the distance between them stays bounded because of the leash.
The two paths are cointegrated, and their difference is the stationary combination.
Two independent walkers without a leash are not: their distance can grow without bound.