Regression trees for regime changes analysis

In the last two decades a large amount of research both in the econometric and statistics literature has been concerned with the detection of structural changes in time series. The most challenging task is to identify multiple breaks occurring at unknown date and most contributions have addressed the case of level shifts. In this context Cappelli et al (2005, 2008) have proposed a computational efficient procedure called ART that employs regression trees to identify the breaks in the mean and their locations. In this streamline this paper focuses on a different problem: the detection of regime changes due to instability in model parameters. At this aim we propose an extension of the ART procedure that uses in the tree growing stage the residuals of models fitted to contiguous subseries obtained by splitting the original series. The best split is the one that maximizes the reduction in the residuals when splitting a node into its offsprings; the location of the splits provides the dates at which the regime change occurred. For the purpose to select of the final number of breaks the Chow test (1960) can be employed: splitting stops if the achieved reduction does not ensure the chosen significance level. Eventually, in order to circumvent the problem of model mispecification, in our programme various models can be assumed growing candidate trees (i.e., sets of breaks). The performance of the proposed approach is evaluated by means of a simulation study. An application to the US labor productivity index is also presented and discussed