This note presents possibly hitherto unnoticed, or only implicitly discussed, properties of the stochastic unit root process developed in Granger and Swanson (1997) and Leybourne, McCabe, and Tremayne (1996).

This paper shows that the recently proposed tests of linear and logarithmic transformations for integrated processes against each other by Kobayashi and McAleer (1999) are severely biased for alternative hypotheses when the true data generating process is a stochastic unit root. An empirical...