Cointegration Tests and VECM for Nonstationary Stock Series

Summary

The note asks how Johansen cointegration analysis differs from fitting a vector autoregression to multiple integrated stock price series. The proposed cointegration approach tests whether a weighted combination of nonstationary series is stationary, then uses those weights to form a basket. The response cautions that a standard VAR generally assumes stationary inputs; fitting it directly to nonstationary price levels can produce misleading relationships.

It recommends testing for cointegration and, if supported, modeling the series with a vector error correction model (VECM). This framework represents both short-run changes and adjustment toward long-run relationships among the series. The response is brief and does not explain test specification, lag selection, cointegration rank, or how to validate a trading basket. Its advice is a high-level distinction: VAR on stationary variables and VECM for cointegrated nonstationary variables, rather than a full comparison of possible VAR formulations.

Key ideas

• Johansen analysis tests whether nonstationary series share stationary linear combinations.
• A standard VAR fitted directly to nonstationary levels can yield spurious relationships.
• When cointegration is supported, a VECM models short-run dynamics and long-run adjustment.
• The note does not cover model selection, validation, or trading implementation.

Tags

# Different ways to identify a co-integrated series?


# Different ways to identify a co-integrated series?












I have been reading and trying out stuff until I am totally confused and back to square one. Could someone please explain the difference between the two methods suggested below?

Suppose I have 10 stock price series that are I(1). I can use Johansen's method to test for co-integration and find appropriate weights for each stock to create a stationary basket from these 10 stocks.

Second approach, I use available VAR (vector auto regression) methods to fit a VAR model on these 10 stocks and find a model that is stable (stationary).

What is the difference between these two approaches? Are they the same because both result in a basket of stocks that is stationary?

## Answer by Swapnil Soni (score 2, accepted)

https://quant.stackexchange.com/a/17276

VAR can be applied only if the input series are stationary otherwise VAR may result in spurious correlation. So just evade it. Now the solution to treat the non stationary series to go for cointegrated series (ca.jo test) and if cointegration is viable then build VECM (Vector Error Correction Mechanism). This incorporate the short and long run relationship between series.

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