Cointegration test is one of important procedures in econometrics. It's confusing.
Here is the basic procedure:
- Test each series to see if both of them are non-stationary, and have the same order of integration.
- If both series are (say) I(1), then construct a VAR model for the 2 variables - this will require choosing the maximum lag-length.
- Test the residuals of the VAR model to see if the errors are (a) independent; and (b) normally distributed.
- Use Johansen's methodology to test if the 2 series are cointegrated.
- In step 6, take account of the structural breaks in the trends of the data, if any. To do this, use the methods introduced by Johansen et al. (2000).
http://davegiles.blogspot.com/2011/05/cointegrated-at-hips.html
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