A Unified Unit Root Test Regardless of Intercept

Using the augmented Dickey-Fuller test to verify the existence of a unit root in an autoregressive process often requires the correctly specified intercept, since the test statistics can be distinctive under different model specifications and lead to contradictory results at times. In this paper, we develop a unified unit root test which not only unifies the specifications of the intercept but also accommodates different degrees of persistence of the underlying process and heteroscedastic errors. A simulation study shows that the proposed test exhibits excellent size control and reasonably good power. In an empirical application, we implement the proposed test to re-examine the presence of unit roots within eleven widely used variables in stock return predictability