A Bayesian Semiparametric Approach for Trend–Seasonal Interaction: an Application to Migration Forecasts

Abstract

Summary We model complex trend–seasonal interactions within a Bayesian framework. The contribution divides into 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 non‐parametric alternatives when the seasonal behaviour is represented by Fourier series of order bigger than 1. Second, the paper uses a Bayesian framework to forecast Swiss immigration, merging the simulations’ outcome with a set of priors derived from alternative hypotheses about the future number of incomers. The result is an effective symbiosis between Bayesian probability and semiparametric flexibility that can reconcile past observations with unprecedented expectations.

Heterogeneous Returns to Scale of Wind Farms in Northern Europe

“…After a series of rearrangements, it can be shown that a penalized likelihood can be used to estimate ( , ) δ θ i j . For all the mathematical details in a frequentist and in a Bayesian framework see (Milivinti and Benini, 2018). The precision of the approximation is function of the total amount of points.…”