Abstract
Linear trend filtering methods are popular due to their over- all simplicity - the model is linear in each segment and there are typi- cally only few segments considered. These segments are defined by unique points where the trend changes its direction - so called changepoints.
In this paper we consider an innovative estimation approach for such mod- els. Our proposal is based on recent developments in the atomic pursuit techniques: we present an estimation algorithm based on the adaptive LASSO penalty and we introduce a fully data-driven method which can be effectively used to fit the continuous linear trend models.
Some statis- tical properties are discussed and the empirical performance is compared with respect to other competitive LASSO based techniques.