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The light curves of variable stars are commonly described using simpletrigonometric models, that make use of the assumption that the model parametersare constant in time. This assumption, however, is often violated, andconsequently, time series models with components that vary slowly in time areof great interest. In this paper we introduce a class of data analysis andvisualization methods which can be applied in many different contexts ofvariable star research, for example spotted stars, variables showing theBlazhko effect, and the spin-down of rapid rotators. The methods proposed areof explorative type, and can be of significant aid when performing a morethorough data analysis and interpretation with a more conventional method.Ourmethods are based on a straightforward decomposition of the input time seriesinto a fast "clocking" periodicity and smooth modulating curves. The fastfrequency, referred to as the carrier frequency, can be obtained from earlierobservations (for instance in the case of photometric data the period can beobtained from independently measured radial velocities), postulated using somesimple physical principles (Keplerian rotation laws in accretion disks), orestimated from the data as a certain mean frequency. The smooth modulatingcurves are described by trigonometric polynomials or splines. The dataapproximation procedures are based on standard computational packagesimplementing simple or constrained least-squares fit-type algorithms.

Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method