Testing the null hypothesis of stationarity against an autoregressive unit root alternative (Q2722253)

Statistical tests for the null hypothesis of stationarity (or trend stationary) by looking at the fluctuation in a (detrended) time series are proposed. The results are applicable to a wide class of time series models. Asymptotic distributions of these tests are derived under both the null hypothesis and the unit root alternative. These limiting distributions are nonstandard and are functions of Brownian motions, involving higher order Brownian bridges. The principle of the approach is general and can be applied to other types of alternatives. Tables of critical values are provided based on the asymptotic null distributions. The consistency of the tests is proved in this paper. It is shown that the limiting distribution has the classical Kolmogorov-Smirnov form. Critical values for the null distribution are calculated. A Monte Carlo experiment is conducted to examine the finite sample performance of these tests. In particular, finite sample size and power are studied. These tests provide a useful complement to the conventional unit root tests, as do other tests for stationarity.