We develop likelihood-based estimators for autoregressive panel data models that are consistent in the presence of time series heteroskedasticity. Bias corrected conditional score estimators, random effects maximum likelihood (RML) in levels and first differences, and estimators that impose mean stationarity are considered for AR(p) models with individual effects. We investigate identification under unit roots, and show that RML in levels may achieve substantial efficiency gains relative to estimators from data in differences. In an empirical application, we find evidence against unit roots in individual earnings processes from the PSID and the Spanish section of the European Panel.