Johansen Cointegration Test and Vector Error Correction Model
Johansen Cointegration Test and Vector Error Correction Model (VECM) · Also known as: Johansen test, VECM, vector error correction model, multivariate cointegration, Johansen Eşbütünleşme Testi ve VECM
The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the short-run dynamics around that equilibrium.
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When to use it
Use the Johansen test when you have several continuous time series that are each integrated of order one, I(1), confirmed by unit-root testing, and you want to know whether they share long-run equilibrium relationships. It needs a reasonably long sample (at least 50 observations, and ideally several hundred) because short series make the test unreliable. The series must not be I(2) or higher, the VAR lag length should be chosen by information criteria, and a deterministic specification should be selected from the five standard cases.
Strengths & limitations
- Tests for multiple cointegrating relationships at once, not just a single pair, within a full system.
- Maximum-likelihood estimation yields the cointegrating vectors and the adjustment speeds together, and supports formal hypothesis tests on them.
- The VECM cleanly separates long-run equilibrium from short-run dynamics, which is valuable for forecasting and structural interpretation.
- Unreliable on short series; with fewer than about 250 observations the ARDL bounds test is preferable.
- Requires all series to be I(1); if any variable is I(2) or higher the test cannot be applied and differencing is needed first.
- Results are sensitive to the chosen lag length and to the deterministic specification (trend and constant).
Frequently asked
What is cointegration?
Cointegration means that two or more individually non-stationary I(1) series move together so that a particular linear combination of them is stationary. That stable combination represents a long-run equilibrium the series keep returning to.
How is the Johansen test different from Engle-Granger?
Engle-Granger handles a single cointegrating relationship between a pair of series, while the Johansen procedure works within a full system and can detect several cointegrating vectors at once, estimating them jointly by maximum likelihood.
Trace test or maximum eigenvalue test — which should I use?
Both test the number of cointegrating vectors but in different ways and can give different answers. Report both statistics; if they disagree, examine the deterministic specification and lag choice rather than picking the convenient result.
When should I use an ARDL bounds test instead?
When the sample is short (roughly under 250 observations) the Johansen test becomes unreliable. In that case the ARDL bounds test is the preferred way to assess a long-run relationship.
Sources
- Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580. DOI: 10.2307/2938278 ↗
- Johansen, S. (1995). Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press. ISBN: 978-0198774501
How to cite this page
ScholarGate. (2026, June 1). Johansen Cointegration Test and Vector Error Correction Model (VECM). ScholarGate. https://scholargate.app/en/finance/johansen-cointegration
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