The statistical study of environmental cycles has received extensive consideration over the years and a variety of models can be applied to data presumed to contain cycles. However, a search in the current literature and textbooks failed to produce a suitable reference that treats the practical aspects of the subject in a systematic manner. The purpose of this paper is to advance a strategy to investigate cycles which may occur at different levels of data aggregation and on different frequencies in a large, multivariate time series context. The strategy is based on the validity for environmental cycles of certain simplifying assumptions and involves extended formal definitions of temporal partitions, cycles, and related concepts. The motivation was provided by the need to interpret the 1979–1981 stretch of the 198 air pollution time series obtained for the Harvard epidemiological study of the health effects of air pollution, which serves as an example to the strategy suggested.