We develop in this paper a test of the null hypothesis that an observed time series is a realisation of a strictly stationary random process. Our test is based on the 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 will have considerable power against an important form of nonstationarity hitherto not considered in the mainstream econometric time series literature -namely 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 by application to three economic data sets.
We do not study PHR's power against the alternative of a process with periodicities in the mean and random variation in the periodic structure, as in REF .
TESTING TIME-SERIES STATIONARITY AGAINST AN ALTERNATIVE WHOSE MEAN IS PERIODIC
Macroeconomic Dynamics
Mathematics