The period with the smallest
is not always "real'',
because "spurious'' periods are introduced by the interplay between
distribution and real periodicity.
The phases of
folded with an arbitrary period are circular data.
This
distribution can be studied with numerous methods for analysing
circular data (e.g. Batshelet 1981; Jetsu & Pelt 1996).
We apply the Deeming (1975) window function
But Eq. (16) cannot separate P_{1} from . The following modification of another method by Tanner (1948) may reveal, if a window P_{0} induces a spurious period P_{1}: (1) Derive . Transform to . (2) Model the with P_{1}, and measure the "phase residuals'' ( ), i.e. the minimum distance for each y_{i} from the model . These are unique, when the distance between data and model is defined as , where and . Transform to . The d_{1} and d_{2} are comparable, because d_{2} is independent of the y_{i} units. The d minimum determines the point closest to uniquely, which yields the phase residuals . Transform to . (3) The linear correlation coefficient ( ) between and is higher for "spurious'' than "real'' periods. Note that we subtract the means from and (Figs. 1q-u, 3q-u, 5q-u and 7q-u), since this does not influence . Our "correlation hypothesis'' is
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