Johansens Cointegration test - VARselect output showing all Lag 1's

I am running a cointegration test on 4 input variables over 1 year and when I run the VARselect it outputs:

AIC(n)  HQ(n)  SC(n) FPE(n)
1      1      1      1

Input - VARselect(Data, lag.max = 10, type = "const")


This is an issue as the minimum K for the ca.jo in RStudio is 2.

I have looked for answers on this site and other papers but cant get a clear answer (or perhaps understand them!).

Question - Can anyone advise how I interpret this or is there a means to choosing a correct lag (say 2)? When I run the ca.jo with 2 or say 4 lags it gives me different hypothesis outcomes.

• Do you understand why ca.jo requires a minimum K of 2? Nov 25 at 12:00
• It is because VARselect does not try to output a result that would necessarily fit into ca.jo. It finds a "best" model, and if that happens to contain 1 lag, then that is it. Might it be that ca.jo only considers a special case of $K\geq2$ while in the general case $K=1$ is also permissible (i.e. it is not incorrect mathematically)? I used to know these things but have forgotten... Nov 26 at 8:15