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Disaggregated data are characterized by a high degree of diversity. Nonparametric models are often flexible enough to capture it but they are hardly interpretable. A semiparametric specification that models heterogeneity directly creates the preconditions to identify causal links. Certainly, the presence of endogenous variables can destroy the ability of the model to distinguish correlation from causality. Triangular varying coefficient models that consider the returns as non-random functions, and at the same time exogeneize the problematic regressors are able to add to the flexibility of a semiparametric specification the causal interpretability. Moreover, they make the necessary assumptions much more credible than they typically are in the standard linear models. The Causality Problem in the Presence of Heterogeneous ReturnsDisentangling causality from correlation is one of the fundamental problems of data analysis. Every time the experimental methodology -typical in some hard sciences -is not applicable, it becomes almost impossible to separate causality from observed correlations using non-simulated data. The only available alternative is to find a set of non testable assumptions that allow to express the causal links as parameters or as functions, and to subsequently find consistent estimators for the conditional moments or distributions that describe the parameters (or functions) of interest. In particular, consider a response Y to be regressed on an explanatory variable W . The assumption that transforms a simple (cor)relation into a causal effect of W on Y , is often called 'exogeneity'. Definition 1. A variable W is weakly exogenous for the parameter of interest ψ, if and only if there exists a re-parametrization λ for the joint density with parameter λ = (λ 1 , λ 2 ) such that 1 We thank an anonymous referee and the participants of the ISNPS 2014 meeting in Cadiz for helpful comments and discussion.

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.

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