Population cycles are ubiquitous in nature and have triggered ecologist's interests for decades. Given a noisy time series exhibiting a spectral peak, how can one decide wether the observed cycles are driven by an external periodic force, or are part of an autonomously emerging limit cycle? Mathematical and numerical results indicate that the spectra and autocovariances of the two signal classes behave qualitatively different and can be used to separate the two cases. I use ROC curves and linear discriminant analysis to evaluate the fidelity of several statistical classifiers.