I am encountering the following problems and I don't really know which model a should pick.
All model selection criteria indicate that I should take the model with 1 lag. After building the VAR(1)-model, I check the LM-test for serial correlation. This test indicates no problems. The portmanteau BDS test for independence (Brock, Dechert, Scheinkman and LeBaron,1996) performs badly, with significant autocorrelations up to 2 and 3 lags, which may indicate a specification error. I am already aware of this topic and I am aware that I should choose LM above the BDS test.
The BDS test however, is known for it's lower power, which roughly means that H0 is picked in favor of H1 (higher risk of type II error). As my portmanteau (BDS) test prefers H1 for autocorrelation up to 2 and 3 lags, I think i should follow my intuition that the model is not correctly specified.
When I create a VAR(4) model, the LM test as well as portmanteau test show the desired results, which means that no autocorrelation can be found. both tests have very high p-values (above 20%) expect for the LM test at Lag 3 (8%).
When I compare the Granger Causalities and Impulse response functions of both models, the VAR(4) model clearly preforms better.
Probably this isn't a good argument, but the R² of the VAR(4) model are higher than the R² of the VAR(1) model.
When I look at the correlograms of the residuals, it's kinda the same.
Does it make sense to prefer the VAR(4) model based on my explanation?