Fisher's g Revisited

In 1929, Fisher proposed a test for periodicity based on the largest periodogram ordinate. If the true frequency lies between two consecutive Fourier frequencies and the signal to noise ratio is low, the test may conclude that there is no periodicity. This loss of power was noted by Whittle in 1952, as well as the necessary assumption that the noise be white. Whittle and subsequent authors suggested remedies for the white noise assumption. This paper proposes simple tests, based on the Fourier coefficients, that is, the Fourier transforms at the Fourier frequencies, that have good power properties at all frequencies.

Automated summary

Fisher proposed a periodicity test in 1929 based on the largest periodogram ordinate, but noted a loss of power in cases where the true frequency falls between two consecutive Fourier frequencies with low signal-to-noise ratio. Whittle and subsequent authors suggested remedies for the white noise assumption. This paper introduces simple tests based on Fourier coefficients that have good power properties at all frequencies.