Detection of the deterministic component from noised time series is a common procedure in the solar–terrestrial coupling problem when climate is modeled, solar activity is analyzed, or a signal associated with helium is extracted. Such series are mostly generated by the superposition of different processes for which the concept of a noise component cannot be determined formally. A method based on the combination of time-series topological embedding in Euclidean space and the identification of a persistent cycle by homology theory methods is proposed. The method application is demonstrated based on actual data.