A strategy for testing the unit root in AR(1) model with intercept: a Monte Carlo experiment

In this paper, we introduce a strategy for testing the unit root hypothesis in a first-order autoregressive process with an unknown intercept where the initial value of the variable is a known constant. In the context of this model the standard Dickey-Fuller test is non-similar, the intercept being the nuisance parameter. The testing strategy we propose takes into account this non-similarity. It is an unusual two-sided test of the random walk hypothesis since it involves two distributions where the acceptance region is constructed by taking away equal areas for the lower tail of the Student's t distribution and the upper tail of the distribution tabulated by Dickey and Fuller under the null hypothesis of unit root. In some cases, this strategy does not allow a direct decision to be taking regarding the existence of a unit root. To deal with these situations we suggest testing for the significance of the intercept, and if doubt persists, we use the Φ1 test proposed by Dickey and Fuller (Econometrica 49 (1981) 1057). Finally, Monte Carlo simulations are used to demonstrate the relevance of non-similarity and to show that the testing strategy is more powerful at most stable alternatives and has less size distortions than the two-sided tests considered by Dickey and Fuller.