<p>Cylindrical time series, obtained from the observation over time of a variable measured as an angle on the unit circle and a real-valued variable, often exhibit patterns consistent with the presence of multiple regimes that alternate randomly over time. In this paper, we address the problem of forecasting future observations of such series. To this end, we consider models specifically designed to account for both the existence of multiple regimes and serial correlation within each regime. The models investigated belong to two main classes: hidden Markov models and threshold autoregressive models. For the former, we explore two alternative joint distributions for the circular and linear components at each time point and propose several estimation strategies. For the latter, we consider two types of partitions associated with the definition of the thresholds, based on both variables. The proposed methods are illustrated through two applications: one involving wind direction and speed measured at a given site, and another concerning the direction and velocity of insect movement.</p>