Abstract: In this thesis, we propose test statistics based on the weighted symmetric estimators for seasonal time series autoregressive models with a unit root and derive. representations for the limit distributions of the estimators and pivotal statistics. The empirical percentiles of the distributions for time series that has a unit root at the seasonal lag are computed for finite samples and limit case by Monte Carlo method. By comparison of the empirical powers, we show that the test statistics with the weighted symmetric estimators are more powerful than that with the ordinary least squares estimators and simple symmetric estimators for the seasonal means model.