This paper addresses the problem of testing for the presence of unit autoregressive roots in seasonal time series with negatively correlated moving average components. For such cases, many of the commonly used tests are known to have exact sizes much higher than their nominal significance level. We propose modifications of available test procedures that are based on suitably prewhitened data and feasible generalized least squares estimators. Monte Carlo experiments show that such modifications are successful in reducing size distortions in samples of moderate size.