  We propose a new semi-parametric approach to the joint segmentation of
multiple series corrupted by a functional part. This problem appears in
particular in geodesy where GPS permanent station coordinate series are
affected by undocumented artificial abrupt changes and additionally show
prominent periodic variations. Detecting and estimating them are crucial, since
those series are used to determine averaged reference coordinates in
geosciences and to infer small tectonic motions induced by climate change. We
propose an iterative procedure based on Dynamic Programming for the
segmentation part and Lasso estimators for the functional part. Our Lasso
procedure, based on the dictionary approach, allows us to both estimate smooth
functions and functions with local irregularity, which permits more flexibility
than previous proposed methods. This yields to a better estimation of the bias
part and improvements in the segmentation. The performance of our method is
assessed using simulated and real data. In particular, we apply our method to
data from four GPS stations in Yarragadee, Australia. Our estimation procedure
results to be a reliable tool to assess series in terms of change detection and
periodic variations estimation giving an interpretable estimation of the
functional part of the model in terms of known functions.
