define your panel structure (cross-sectional and time identifiers) with xtset command and then run the xtserial command: a significant test statistic indicates the presence of serial correlation.
It's a community-contributed program-if you don't have it in your stata - you can install it - just type
This test is used to test for autocorrelation in panel data. This test is considered robust because it works with lesser assumptions on the behavior of the heterogeneous individual effects.
Yes, there is a Wooldridge test for autocorrelation in panel data. The test is used to detect first-order autocorrelation in the errors of a panel data model. The test is based on the residuals from the first-differenced regression of the dependent variable on its lagged values.