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Zbl 0669.62088
Chiu, Shean-Tsong
Detecting periodic components in a white Gaussian time series. (English)
[J] J. R. Stat. Soc., Ser. B 51, No.2, 249-259 (1989). ISSN 0035-9246

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.

MSC 2000:: *62M15 Spectral analysis of processes
62E20 Asymptotic distribution theory in statistics

Keywords: detecting periodic components; Fourier transform; outliers; robust estimate; time series; tests for periodic components; white Gaussian series; maximum periodogram; trimmed mean of the periodograms; Fisher's test; asymptotic powers; sinusoidal wave; simulation results; alternatives of multiple peaks; detecting multiple peaks

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