Choosing Cointegration Tests: Specification, Lags, and Consensus

Summary

This note compares Engle–Granger with Johansen for testing cointegration between two variables. It does not establish that either test is universally more powerful or more prone to false positives or negatives. Instead, it points readers toward a comparison that also includes the Phillips–Ouliaris test, and suggests checking whether the tests agree when they are applied to the same data.

The central practical lesson is that test setup can matter more than the choice among test families. The deterministic terms and lag structure need to fit the data-generating process; misspecification can make conclusions unreliable. The document offers no empirical comparison, performance measures, or worked example, and its suggestion to seek consensus is a rule of thumb rather than a formal decision procedure. Results from multiple tests should therefore be interpreted alongside model assumptions and diagnostics, rather than treated as independent votes that settle whether a relationship is genuinely cointegrated.

Key ideas

• No single cointegration test is identified as universally superior for two variables.
• Phillips–Ouliaris is presented as a useful additional comparison with Engle–Granger and Johansen.
• Agreement among several test results may help flag robust findings, but it is not a formal selection rule.
• Choosing deterministic components and lags to suit the model is essential to credible inference.

Tags

# What's the practical difference between the Johansen vs Engle-Granger tests for cointegration?


# What's the practical difference between the Johansen vs Engle-Granger tests for cointegration?












For the two-variable case, what are the practical differences between using the Engle-Granger procedure versus the Johansen test for cointegration? Is one universally more powerful than the other? Will one give more false positives or false negatives than the other? Should Johansen always be preferred?

## Answer by d8aninja (score 1)

https://quant.stackexchange.com/a/25873

Neither. This question and its references suggest that the Philipis Ouliaris (1990) test is a significant improvement over EG ADF and JCT. Given the automation, you should probably run all three tests and see if there's any consensus.

It actually surprises me there isn't (at least in Eviews) a function that shows a table of the EG, JCT, and PO results next to each other for comparison. This is how the lag selection table is presented, which makes it easy to find consensus in the criteria.

As always, however, I'd like to echo a statement made in the question linked above:

> "The main question is whether you use the correct specification of deterministic components and lags. Using a badly specified test will probably be more harmful than using a 'bad' test on the correct model."

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.