A Test for Non-Stationarity of Time-Series

Summary We consider the problem of testing a given time-series for stationarity. The approach is based on evolutionary spectral analysis, and the proposed method consists essentially in testing the “homogeneity” of a set of evolutionary spectra evaluated at different instants of time. Using a logarithmic transformation, we show that the mechanics of the test are formally equivalent to a two-factor analysis of variance procedure when the residual variance is known, a priori. In addition to testing stationarity, the analysis provides also a method for testing whether the observed series fits a “uniformly modulated” model, and a test for “randomness” (constancy of spectra).