Use Cointegration Tests, Not Correlation, to Assess Spurious Regression Risk

Summary

The note addresses whether a high Pearson correlation between two financial time series can identify spurious cointegration. Its response points instead to testing the cointegration rank with the Johansen method. Correlation alone is not presented as a reliable diagnostic for whether a long-run equilibrium relation exists.

The explanation distinguishes cases by integration properties and cointegration rank. If both series are stationary, the response says there is no cointegration vector, though short-run dynamics may still exist. If both are integrated of order one and no cointegration vector is present, regression in levels can be spurious, so modeling their differences is relevant. A reduced-rank cointegration matrix for integrated series indicates a cointegrating relation. The note gives a compact conceptual guide, but no test statistics, critical values, model specifications, or practical validation procedures.

Key ideas

• High Pearson correlation does not establish that two series are cointegrated.
• Johansen methods test the rank of the cointegration matrix.
• Non-cointegrated I(1) series can produce spurious regressions when modeled in levels.
• Stationary series may still have short-run dynamics even without a cointegration vector.

Tags

# High correlation will help detect spurious regression over cointegration?


# High correlation will help detect spurious regression over cointegration?












I'm analyzing two financial time series with Johansen method. A high Correlation coefficient using the Pearson method will help me to detect spurious cointegration models to avoid? If this is not the case, which is the best method would provide clue about it? Thank you

## Answer by Analyst (score 2)

https://quant.stackexchange.com/a/14293

I would say that you can use Johansens methods to test for rank of co-integration matrix. There are tests for that. If there is no co-integration vector present and both series are I(0) then there is no co-integration. Series still might have some short-run dynamics.

If series are I(1) and no con-integration vector is present then modeling these series by their levels and not differences can cause spurious regressions.

If series are I(1) and their co-integration matrix has reduced rank then they have one co-integration relation.

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