A Bayesian approach for the segmentation of series with a functional effect

In some application fields, series are affected by two different types of effects: abrupt changes (or change-points) and functional effects. We propose here a Bayesian approach that allows us to estimate these two parts. Here, the underlying piecewise-constant part (associated to the abrupt changes) is expressed as the product of a lower triangular matrix by a sparse vector and the functional part as a linear combination of functions from a large dictionary where we want to select the relevant ones. This problem can thus lead to a global sparse estimation and a stochastic search variable selection approach is used to this end. The performance of our proposed method is assessed using simulation experiments. Applications to three real datasets from geodesy, agronomy and economy fields are also presented.