Testing time-series stationarity against an alternative whose mean is periodic

We develop a test of the null hypothesis that an observed time series is a realization of a strictly stationary random process. Our test is based on t he result that the kth value of the discrete Fourier transform of a sample frame has a zero mean under the null hypothesis. The test that we develop w ill have considerable power against an important form of nonstationarity hi therto not considered in the mainstream econometric time-series literature, that is, where the mean of a time series is periodic with random variation in its periodic structure. The size and power properties of the test are: investigated and its applicability to real-world problems is demonstrated b y application to three: economic data sets.