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Interpreting Johansen Cointegration Rank and Choosing a VECM

Article Quant Q&A · Author: Anna
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Summary

The document raises how to interpret a Johansen test that indicates cointegration rank of at least five among nine time series. It asks whether the test can identify which individual series are cointegrated, whether ADF or another test would help, and whether a VECM suits the goal of modeling the series with a VAR.

It offers no answers, test output, data description, or empirical evidence. The key methodological issue is that Johansen rank describes the number of independent long-run relationships in the system; it does not directly label particular series as cointegrated pairs. A VECM is generally used when variables are integrated and cointegrated, while an ordinary VAR in differences or levels may be appropriate under different assumptions. The document is a question rather than a worked analysis, so it does not establish the integration properties or model specification needed to make a recommendation.

Key ideas

  • Johansen cointegration rank counts independent long-run relationships across a system of series.
  • The reported rank does not identify specific cointegrated pairs by itself.
  • ADF tests can assess individual series for unit roots but do not reveal the system's cointegrating relationships.
  • A VECM can represent short-run dynamics and long-run adjustment when series are cointegrated.
  • The document provides no data or test details to validate a model choice.

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# Johansen cointegration test interpretation in R


# Johansen cointegration test interpretation in R












I want to test my time series for cointegration using the Johansen test in R. I got the following result and so I know now that at least 5 out of 9 of my time series are cointegrated. My question is, how to understand which one of them are cointegrated and which one aren't.

If it's not possible to answer my question within this particular test, maybe the ADF test (or any other test) will help me with this problem?

My primary goal was to build up a VAR for this time series. So my next question will be if it's appropriate to use the VECM for these series in order to reach my goal.

I'll appriciate any help and/or advice!

Thanks,

Anna.

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