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Hello,
I would like to estimate a VAR model for four time series. The series are I(1) processes and potentially cointegrated. To confirm I chose the Johansen cointegration test. Since I don't know whether the model should include a deterministic/ stochastic trend or intercept for the cointegrating relationship or the vector autoregression, I opted for summary results. Herein lies the problem: depending on the lag length for the differenced terms in the equation, I get different results for the type of model to choose based on trace/max-eigenvalue. However, I can only test for lag length criteria after actually making the VAR (prior to which I have to decide on intercepts/trends to be included). I need a multivariate test statistic that helps me to decide on model type as well as lag length. I could produce the summary test results for several lag lengths and then select the one with the smallest SBIC or other criterion followed by a lag exclusion test, but I am not confident that this is appropriate. Specifically, I'm not sure what impacts more on the information criteria provided: lag length or model type.
Unfortunately, economic theory is of little help in determining an appropriate lag length/model type a priori. However, it may be assumed that the maximum lag length considered is three (also for practical reasons since larger models would quickly eat up degrees of freedoms due to the number of required coefficients to be estimated. The number of observations per series is n = 120). Any input is greatly appreciated
Regards
Florian

I have the impression that you try to integrate what is actually a series of decisions into one. You don't mention if you did any uni-variate tests in your variables before you embark on specifying your VAR/VEC model. Did you do any unit root tests (e.g. ADF)?

Deterministic terms:

Did the results from the series indicated that any series contained an intercept or a linear trend? If not then there is no use in including a trend in your VAR model, since all unit roots and co-integration tests are sensitive in the model specification and THIS IS the reason you get mixed results.

Lag Order Selection:

The ADF tests automatically select lag lengths for each variable. Use that range to select the best model from. E.g. the lag length in your variables ranges from 2 to 6 then estimate VAR models with all 2, 3, 4, 5, 6 lags. Then use the model selection criteria (e.g. BIC, AIC) to choose the optimal length.

Check for Normality, Homoskedasticity and Serial Correlation in the resiluals (misspecification tests).

THEN, having selected a lag length according to both the misspecification tests and the model selection criteria you use THAT model for statistical inference and co-integration tests.

Again, FIRST you specify your model and THEN you perform co-integration tests. You have mixed results because you use different models - without actually testing WHICH ONE is better statistically specified.