Fast and Statistically Optimal Period Search in Uneven Sampled Observations

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Abstract
The classical methods for searching for a periodicity in uneven sampled observations suffer from a poor match of the model and true signals and/or use of a statistic with poor properties. We present a new method employing periodic orthogonal polynomials to fit the observations and the analysis of variance (ANOVA) statistic to evaluate the quality of the fit. The orthogonal polynomials constitute a flexible and numerically efficient model of the observations. Among all popular statistics, ANOVA has optimum detection properties as the uniformly most powerful test. Our recurrence algorithm for expansion of the observations into the orthogonal polynomials is fast and numerically stable. The expansion is equivalent to an expansion into Fourier series. Aside from its use of an inefficient statistic, the Lomb-Scargle power spectrum can be considered a special case of our method. Tests of our new method on simulated and real light curves of nonsinusoidal pulsators demonstrate its excellent performance. In particular, dramatic improvements are gained in detection sensitivity and in the damping of alias periods.

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