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

Abstract

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 Φ 1 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.