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Fisher's g Revisited
Author(s) -
Quinn Barry G.
Publication year - 2021
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12437
Subject(s) - white noise , mathematics , fourier transform , fourier series , fourier analysis , noise (video) , statistics , discrete time fourier transform , power (physics) , mathematical analysis , short time fourier transform , computer science , physics , artificial intelligence , image (mathematics) , quantum mechanics
Summary 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.