Tests of the null hypothesis of stationarity against the unit root alternative play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asymptotic critical values for stationarity tests may cause extreme size...

This study analyzes the size and power of tests of the null of stationarity against the unit root alternative. Existing evidence is limited to processes with roots between 0 and 0.7. In sharp contrast, virtually all applications of economic interest involve null hypotheses much closer to 1. We...

This article proposes a locally best invariant test of the null hypothesis of seasonal stationarity against the alternative of seasonal unit roots at all or individual seasonal frequencies. An asymptotic distribution theory is derived and the finite-sample properties of the test are examined in...

This paper generalizes the univariate results of Chan and Tran (1989, <italic>Econometric Theory</italic> 5, 354–362) and Phillips (1990, <italic>Econometric Theory</italic> 6, 44–62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and...