Abstract
Abstract. Spectral analysis is a well‐established procedure for detecting harmonic signals in a noisy environment. Much research has been done on methods that use second‐order statistics (i.e. the autocovariance function and power spectrum) such as Whittle's test, Bartlett's test, Hannan's test and the Priestley P(Λ) test. When the noise is non‐Gaussian, statistics of order greater than two can provide more information to detect the periodicities in noisy data. We direct our main attention to the third (fourth) order cumulant and bispectral (trispectral) methods. New test statistics are derived and are shown to be more powerful than other methods based on second‐order statistics under a mixed spectrum condition. The asymptotic power functions of the new test statistics and other tests are studied. Some Monte Carlo simulations are used to evaluate the performance of the new methods with moderate sample sizes.
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