Identification of aperiodic seasonality in non-Gaussian time series

Time series that arise from biological experimentation can exhibit seasonality where the lengths of the seasons may vary. In addition, such time series may not be stationary with respect to either mean, variance, or autocorrelation, thus making the usual waveform-fitting techniques inappropriate. An agglomerative clustering algorithm for identifying seasons in such series is proposed, consisting of an initialization step, iterative steps where clusters are combined into larger clusters, and a stopping rule for the iteration. The clusters can be associated with seasons or phases, and biological cycles can be identified from the phases. Results of a simulation and an analysis of luteinizing hormone concentrations are presented.