# Johansen test conditions and Breusch-Godfrey LM test

I am a student from Belgium and I am writing a thesis about the relationship between credit aggregates and property prices. I examine the Granger causality between the two variables and I also do some conintegration tests. I have a question about the latter.

What are the conditions for doing a Johansen cointegration test? Do the residuals need to be tested for serial correlation before you can do the test? Because sometimes I just don't find a model where this is the case. Or do the residuals don't need to be uncorrelated?

Are there other conditions regarding the Johansen test?

When I test for residual autocorrelation I use the Breusch-Godfrey LM test. What is the lag-order that I need to choose for this test? I have 158 observations in my time series. If I do the varselection in levels I always used a maximum lag of 12 and for the Breusch-Godfrey LM test I always used 6. Is this correct?

If so: where do I find references to support these conclusions?

For your first question, yes, you need to have uncorrelated residuals. In general, your need to determine the lag order of the VAR THEN your perform a cointegration test. This means that there must be no residual autocorrelation in your VAR model (if there still is, you need to increase the lag order. Which lag order to increase to will depend on your information criteria such as AIC, BIC, etc.). Once the VAR lag order is selected, you perform the cointegration test (assuming normally distributed residuals of course). Also note that the Johansen test statistic converges very slowly (even a sample size of 300 is considered to be small) hence the test result may not be reliable.

For your second question, there are only some general rules. Some may use lag of 12 since one may have yearly data. There may be other general rules btu I was taught to choose the maximum PACF. I have also heard of performing different LM tests with different lag then choose the one with the highest adjusted R-squared or the lowest AIC or SC.