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Wide-sense cyclostationary processes are an important class of non-stationary processes that have a periodic structure in their first- and second-order moments. This article extends the notion of cyclostationarity (in the wide sense) to processes where the mean and covariance functions might depart from strict periodicities and constant amplitudes. Specifically, we propose a novel and flexible class of processes that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the classical cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using synthetic signals and a physical signal, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae.
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