The current paper models complex trend-seasonal interactions within a Bayesian framework. The contribution divides in two parts. First, it proves, via a set of simulations, that a semiparametric specification of the interplay between the seasonal cycle and the global time trend outperforms parametric and nonparametric alternatives when the seasonal behavior is represented by Fourier series of order bigger than one. Second, the paper uses a Bayesian framework to forecast Swiss immigration merging the simulations' outcome with a set of priors derived from alternative hypothesis about the future number of incomers. The result is an effective symbiosis between Bayesian probability and semiparametric flexibility able to reconcile past observations with unprecedented expectations.