# How many lags should I include in a VAR model?

When building a VAR-model with six variables and 117 observation, I had the following situation: after building a VAR(1), the overall portmanteau test says that the residuals are OK ($p=0.85$, $p_{adjusted}=0.22$). But when I have a look at the single residuals the ACFs all look white noise except one of the six in my case. For this only one it seems like I need a VAR(2) -- and portmanteau test for this single residual shows: $p=0.067$, $p_{adjusted}=0.029$.

I'm unsure what to do in this situation. I experienced the same situation in another VAR where one residual looked like including 5 lags.

So the first question is, how do I decide if 1 lag is enough or if I need 2 lags?

Next: If I decide that it takes 2 lags, do I then have to let the model estimate the whole matrix even if there is only one variable that needs the second lag? Or is it reasonable to allow for the matrix of the second lags only the specific row (and/or column) belonging to this variable? Like in the picture below - imagine only variable E shows elevated autocorrelation at lag 2; the picture is only for showing the problem, normally there is a constant included and deterministic trend terms, too.

What to do in the case of one residual showing only lag 5 to include additionally? Then I would not include the matrices for lags 2, 3 and 4 and only for 5?

What goes in the same direction: if I first include only intercepts and deterministic trends and see that some residuals are already WN, then does it make sense to include any predictors for them? Should I include higher lags only for the variables where the residuals show it?

NOTE: $p$ and $p_{adjusted}$ are calculated as follows:

• @RichardHardy: maybe you can help me again :) – eski Mar 20 '15 at 16:11
• I wonder how is p_adjusted defined? – Richard Hardy Mar 20 '15 at 21:03