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Debate over the existence of branches in the stellar activity-rotationdiagrams continues. Application of modern time series analysis tools to studythe mean cycle periods in chromospheric activity index is lacking. We developsuch models, based on Gaussian processes, for one-dimensional time series andapply it to the extended Mount Wilson Ca H&K sample. Our main aim is to studyhow the previously commonly used assumption of strict harmonicity of thestellar cycles as well as handling of the linear trends affects the results. Weintroduce three methods of different complexity, starting with the simpleBayesian harmonic model and followed by Gaussian Process models with periodicand quasi-periodic covariance functions. We confirm the existence of twopopulations in the activity-period diagram. We find only one significant trendin the inactive population, namely that the cycle periods get shorter withincreasing rotation. This is in contrast with earlier studies, that postulatethe existence of trends in both of the populations. In terms of rotation tocycle period ratio, our data is consistent with only two activity branches suchthat the active branch merges together with the transitional one. The retrievedstellar cycles are uniformly distributed over the R'HK activity index,indicating that the operation of stellar large-scale dynamos carries smoothlyover the Vaughan-Preston gap. At around the solar activity index, however,indications of a disruption in the cyclic dynamo action are seen. Our studyshows that stellar cycle estimates depend significantly on the model applied.Such model-dependent aspects include the improper treatment of linear trends,while the assumption of strict harmonicity can result in the appearance ofdouble cyclicities that seem more likely to be explained by thequasi-periodicity of the cycles.

Estimating activity cycles with probabilistic methods II. The Mount Wilson Ca H&K data