Estimating activity cycles with probabilistic methods

Context. Period estimation is one of the central topics in astronomical time series analysis, in which data is often unevenly sampled. Studies of stellar magnetic cycles are especially challenging, as the periods expected in those cases are approximately the same length as the datasets themselves. The datasets often contain trends, the origin of which is either a real long-term cycle or an instrumental effect. But these effects cannot be reliably separated, while they can lead to erroneous period determinations if not properly handled. Aims. In this study we aim at developing a method that can handle the trends properly. By performing an extensive set of testing, we show that this is the optimal procedure when contrasted with methods that do not include the trend directly in the model. The effect of the form of the noise (whether constant or heteroscedastic) on the results is also investigated. Methods. We introduced a Bayesian generalised Lomb-Scargle periodogram with trend (BGLST), which is a probabilistic linear regression model using Gaussian priors for the coefficients of the fit and a uniform prior for the frequency parameter. Results. We show, using synthetic data, that when there is no prior information on whether and to what extent the true model of the data contains a linear trend, the introduced BGLST method is preferable to the methods that either detrend the data or opt not to detrend the data before fitting the periodic model. Whether to use noise with other than constant variance in the model depends on the density of the data sampling and on the true noise type of the process.