Cointegration Test (Johansen / Engle-Granger)
Also known as: Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)
The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).
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When to use it
Use a cointegration test when you have two or more continuous time series that are each integrated of order one — that is, non-stationary in levels but stationary after first differencing — and you want to know whether they share a long-run equilibrium. A reasonable span of observations is needed (at least about 50); confirm each series is I(1) with an ADF or Phillips-Perron test first and choose the lag length by AIC or BIC. It is not appropriate when the series are already stationary (I(0)), in which case a level VAR suffices.
Strengths & limitations
- Detects a genuine long-run equilibrium between trending series that would otherwise look spuriously related.
- The Johansen system approach can identify more than one cointegrating relationship among several series at once.
- A positive result justifies moving to a vector error-correction model that separates short-run dynamics from long-run adjustment.
- Requires every series to be integrated of order one; if the series are stationary, no cointegration is sought and a level VAR is enough.
- The Johansen test suffers severe size distortion in small samples (n < 50), where an ARDL bounds test is preferable.
- Results are sensitive to the chosen lag length and deterministic terms (trend/intercept specification).
Frequently asked
What does it mean for series to be cointegrated?
It means that although each series is individually non-stationary (it wanders with a stochastic trend), a particular linear combination of them is stationary. That stationary combination represents a long-run equilibrium the series return to, so they cannot drift apart indefinitely.
When should I use the Johansen test versus Engle-Granger?
Engle-Granger is a simple two-step residual test for a single cointegrating relationship between two series. The Johansen procedure is a system approach that can detect and count multiple cointegrating relationships among several series simultaneously and is generally preferred when more than two variables are involved.
What do I do after finding cointegration?
If the series are cointegrated, estimate a vector error-correction model (VECM), which captures both the short-run dynamics and the speed of adjustment back to the long-run equilibrium. You can then test Granger causality among the variables.
Why does my small sample give unreliable results?
The Johansen test exhibits severe size distortion in small samples (fewer than about 50 observations), so it over-rejects the no-cointegration null. With short series, an ARDL bounds test is the more reliable alternative.
Sources
- Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254. DOI: 10.1016/0165-1889(88)90041-3 ↗
- Engle, R. F. & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276. DOI: 10.2307/1913236 ↗
How to cite this page
ScholarGate. (2026, June 1). Cointegration Test (Johansen / Engle-Granger). ScholarGate. https://scholargate.app/en/econometrics/cointegration-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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