On period determination methods

It is noted that the two large families of period determination techniques based on the Fourier transform and on the nonparametric algorithms derived from the theta-criterion by Lafler and Kinman (1965) are not equivalent to each other under general conditions. Instead, at best, all criteria may be expressed as the ratio of two quadratic forms. Numerical simulations have been conducted in order to compare the performance of Deeming's (1975) Fourier method, Burki et al.'s (1978) autocorrelation method, Lafler and Kinman's (1965) method, and the Renson (1978) and Stellingwerf (1978) methods. When applied to single-periodic phenomena, the tests indicate that none of the methods is clearly superior.