A comparison of two modified stationarity tests. A Monte Carlo study

- We assess the small sample properties of a modified version of the Xiao stationarity test.
- We compare the performance of this test to the KPSS stationarity test.
- We recommend the KPSS test.

To specify an econometric model with time series data, it is important to determine the order of integration of the variables in the model. In this paper, using a complete set of Monte Carlo experiments, we compare the behaviour of two stationarity tests, the Xiao test (Sn) and the KPSS (Kwiatkowski, Phillips, Schmidt and Shin) test, using an alternative estimator of the long-run variance to those used in the original version of the tests, to recommend which one to use in practice. First, we compare the small sample properties of the original Sn test with those of its modified version. We conclude that this modified version has a better size versus power trade-off than the original test. So, second, we compare the finite sample properties of the modified Sn and the modified KPSS. Since the modified KPSS exhibits higher power and size, we conduct a second experiment determining the critical value of each test, in such a way that the power of both tests coincides at 0.5, and then we examine their size for some local-to-unity values. The results show that, in most cases, the performance of the modified KPSS test dominates that of the modified Sn test.