The Stochastic Unit Root Model and Fractional Integration: an Extension to the Seasonal Case

In a recent paper, Yoon (2003) shows that the Stochastic Unit Root (STUR) model is closely related to long memory processes, and, in particular, that it is a special case of an I(d) process, with d = 1.5. In this paper we further examine this issue by using parametric and semiparametric techniques for modelling long memory. In particular, we extend the analysis by considering both non-normality and seasonality, and shed light, theoretically and by means of Monte Carlo methods, on the relationship between the seasonal STUR and the seasonal I(d) models. The results show that, even in the case of I(1.5) underlying processes, the methods, which are specifically designed for testing I(d) statistical models are not appropriate for testing the STUR model. Moreover, they have in some cases very low power against STUR alternatives.