A procedure of multiple period searching in unequally spaced time-series with the Lomb-Scargle method

Periodogram analysis of unequally spaced time-series, as part of many biolo gical rhythm investigations, is complicated. The mathematical frameworkis s cattered over the literature, and the interpretation of results is often de batable. In this paper, we show that the Lomb-Scargle method is the appropr iate tool for periodogram analysis of unequally spaced data. A unique proce dure of multiple period searching is derived, facilitating the assessment o f the various rhythms that may be present in a time-series. All relevant ma thematical and statistical aspects are considered in detail, and much atten tion is given to the correct interpretation of results. The use of the proc edure is illustrated by examples, and problems that may be encountered are discussed. It is argued that, when following the procedure of multiple peri od searching, we can even benefit from the unequal spacing of a time-series in biological rhythm research.