test serial correlation for panel data for large T and small N

[Mahvish Faran Khan]

Hi

I am using xtpcse for estimating my unbalanced panel (T=800 and N=9).
What tests are available to test autocorrelation?
I have used xtserial and it rejects the null of no first order serial correlation so I used xtpcse, corr(ar1) and xtpcse(psar1) as well but how to know whether the autocorrelation in my data is of order 1 or some other order?

Thanks

[Phil Bromiley]

Some like AIC/BIC to choose the order of the serial correlation.

[Mahvish Faran Khan]

Can I use that for panel data also?