In this paper, a mean adjustment scheme for unit root tests in the presence of deterministic seasonality is discussed. The Cauchy estimator for autoregressive processes provides some advantages in the application to unit root tests. In particular, it allows for asymptotically standard normal tests and does not require any tabulation of the critical values. The approach can also be employed for testing seasonal unit root. In both cases, a special scheme of mean adjustment based on recursive coefficients, so-called recursive mean adjustment, is essential to maintain the martingale property of regressors. However, the straightforward recursive estimation of seasonal dummies in the case of deterministic seasonal effects leads to a strong positive bias of the estimated autoregressive parameter and therefore to invalid tests. This paper shows how to overcome this problem and to use the Cauchy estimator for unit root testing in the presence of deterministic seasonality.
