title: A procedure of multiple period searching in unequally spaced time-series with the Lomb-Scargle method.
abstract: Periodogram analysis of unequally spaced time-series, as part of many biological rhythm investigations, is complicated. The mathematical framework is scattered over the literature, and the interpretation of results is often debatable. In this paper, we show that the Lomb-Scargle method is the appropriate tool for periodogram analysis of unequally spaced data. A unique procedure of multiple period searching is derived, facilitating the assessment of the various rhythms that may be present in a time-series. All relevant mathematical and statistical aspects are considered in detail, and much attention is given to the correct interpretation of results. The use of the procedure is illustrated by examples, and problems that may be encountered are discussed. It is argued that, when following the procedure of multiple period searching, we can even benefit from the unequal spacing of a time-series in biological rhythm research.
authors.affiliation: Unit for Experimental Psychiatry, Univ. of Pennsylvania School of Medicine, Philadelphia, USA. VDongen@Mail.Med.UPenn.edu
authors.forename: H P
authors.initials: HP
authors.lastname: Van Dongen
authors.forename: E
authors.initials: E
authors.lastname: Olofsen
authors.forename: J H
authors.initials: JH
authors.lastname: VanHartevelt
authors.forename: E W
authors.initials: EW
authors.lastname: Kruyt
mesh_terms: D001831:Body Temperature / Q000502:physiology; D002940:Circadian Rhythm; D003627:Data Interpretation, Statistical; D005583:Fourier Analysis; D006801:Humans; D006854:Hydrocortisone / Q000378:metabolism; D016018:Least-Squares Analysis; D008433:Mathematics; D010507:Periodicity; D013997:Time Factors; D014872:Water Movements
chemical_list: D006854:Hydrocortisone