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A condition where nonstationary series share a stable long-run equilibrium, with some linear combination being stationary.
DESCRIPTION
Cointegration occurs when individually nonstationary time series move together so that a linear combination is stationary. It implies a long-term equilibrium relationship despite short-run deviations. Testing commonly uses Engle–Granger or Johansen procedures. Cointegrated series are modeled with error-correction terms to capture both long-run equilibrium and short-run dynamics. It is central in econometrics for modeling prices, exchange rates, and macroeconomic aggregates.
ALTERNATIVE DEFINITIONS
Penn State STAT 510
Two or more nonstationary time series are said to be cointegrated if some linear combination of them is stationary.
Classic textbook definition emphasizing linear combination stationarity.
Wikipedia
Two or more time series are cointegrated if they share a common stochastic drift and a linear combination is stationary.
Mentions common stochastic trend along with stationarity of a linear combination.
Forecasting: Principles and Practice
If two time series are both non-stationary but a linear combination of them is stationary, the series are said to be cointegrated.
Concise explanation used in forecasting context.
RELATED TERMS
Stationarity Unit Root Engle–Granger Test Johansen Test Error Correction Model Vector Autoregression Order of Integration ADF Test Long-run Equilibrium
COMPETING TERMS
Correlation Spurious Regression
KNOWLEDGE AREAS
TARGET AUDIENCE
EXTERNAL SOURCES
- Wikipedia - Cointegration
- Penn State STAT 510 - Course module on cointegration
- Hyndman & Athanasopoulos - Forecasting-focused explanation
TOP QUESTIONS
What is cointegration in time series?
It describes nonstationary series that share a long-run equilibrium, where a linear combination is stationary.
Category: Definition
Why is cointegration important?
It allows modeling long-run relationships and avoiding spurious regression. It supports error-correction models for realistic dynamics.
Category: Relevancy
How do you test for cointegration?
Use Engle–Granger two-step or Johansen tests, after verifying integration orders.
Category: HowTo
What is an Error Correction Model (ECM)?
An ECM includes a term proportional to the deviation from long-run equilibrium, enabling short-run adjustments.
Category: Concepts
Can more than two series be cointegrated?
Yes, multivariate cointegration allows several cointegrating vectors (Johansen framework).
Category: Concepts
What happens if I ignore cointegration?
You risk spurious regression and biased inference. Differencing may remove valuable long-run information.
Category: Risk
Do cointegrated series require differencing?
Models include differenced terms and an error-correction term, preserving long-run information.
Category: Practice
Is cointegration the same as correlation?
No, correlation is a contemporaneous association; cointegration concerns long-run equilibrium in nonstationary series.
Category: Misunderstanding
What software supports cointegration testing?
statsmodels, EViews, R’s urca, and Stata implement Engle–Granger and Johansen tests.
Category: Tooling