Theoretical Regression Trees for multiple structural change models analysis

The analysis of structural-change models is nowadays a popular subject of research both in econometric and statistical literature. The most challenging task is to identify multiple breaks occurring at unknown dates. In case of multiple shifts in mean Cappelli and Reale (2005) have proposed a method called ART that employs regression trees to estimate the number and location of breaks. In this paper we focus on regime changes due to breaks in the coefficients of a parametric model and we propose an extension of ART that addresses this topic in the general framework of the linear model with multiple structural changes. The proposed approach considers in the tree growing phase the residuals of parametric models fitted to contiguous subseries obtained by splitting the original series whereas tree pruning together with model selection criteria provide the number of breaks. We present simulation results pertaining to the behavior of the proposed approach as well as an empirical application to the time series of the car drivers killed or seriously injured in Great Britain in traffic accidents aiming at evaluating the impact of UK introduction of compulsory seatbelt wearing.