Testing for Unit Roots in Time Series with Nearly Deterministic Seasonal Variation

This paper considers the problem of testing for thepresence of unit autoregressive roots in time series with seasonal components that are arbitrarily close to being deterministic. In particular, the performance of several test criteria for seasonal and non-seasonal unit autoregressive roots is investigated in the case tha tthe data generating mechanism involves a negatively correlated seasonal moving average component. For such cases, many of the commonly used tests are known to have exact sizes much higher than their nominal level. Modifications of available test procedures, based on suitably prewhitened data and feasible generalized least squares estimates, are proposed which substantially reduce size distortions while retaining reasonable power.