Testing temporal constancy of the spectral structure of a time series

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades We develop a nonparametric test for stationarity against the alternative of smoothly time-varying spectral structure The test is based oil a comparison between the sample spectral a density calculated locally oil a moving window of data and a global spectral density estimator based oil the whole stretch of observations Asymptotic properties of the nonparametric c,,estimators involved and of the test statistic under the null hypothesis of stationarity we derived Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated