Detecting Periodic Components in a White Gaussian Time Series

Abstract

SUMMARY A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest that the proposed test is more powerful than Fisher's test against the alternatives of multiple peaks. The problem of detecting multiple peaks is also discussed.