Reviving the maximum likelihood method for detecting dominant periodicities from near-periodic signals

Many naturally occurring signals exhibit near, rather than perfect, periodicity, as a result of variation in cycle length (CL). The accuracy of methods to detect near-periodic signals is typically not evaluated against known CL variations which may compromise their performance. The maximum likelihood method (ML) proposed by Noll to evaluate periodicity involves block averaging which, with smoothing may make it robust to CL variations. In this paper, we revive the ML method and present it as a robust candidate for detecting near-periodicity. We propose to compare the performance of ML to conventional periodicity detection methods by testing against synthetic periodic data with varying CL and noise. Our results indicate that the ML method is significantly more accurate than conventional methods. We also demonstrate a substantial influence of periodic CL fluctuations on the accuracy of all methods.