Testing for a Jump in the Spectral Function

SUMMARY The problem of testing for a jump in the spectral function of a stationary time series is considered. The test based on the greatest periodogram ordinate divided by an estimate of the spectral density is discussed and a modification is suggested which consists essentially of taking out regression on the harmonic with frequency 2πj/n, before computing the estimate of the spectral density at that frequency. The regression can be approximately effected by using the corresponding periodogram ordinate.