Regression trees for regime changes analysis

In the last two decades a large amount of researchboth in the econometric and statistics literature has beenconcerned with the detection of structural changes in time series.The most challenging task is to identify multiple breaks occurringat unknown date and most contributions have addressed the case oflevel shifts. In this context Cappelli et al (2005, 2008)have proposed a computational efficient procedure called ART thatemploys regression trees to identify the breaks in the mean andtheir locations. In this streamline this paper focuses on adifferent problem: the detection of regime changes due toinstability in model parameters. At this aim we propose anextension of the ART procedure that uses in the tree growing stagethe residuals of models fitted to contiguous subseries obtained bysplitting the original series. The best split is theone that maximizes the reduction in the residuals when splitting anode into its offsprings; the location of the splits provides thedates at which the regime change occurred. For the purpose to select of the final number of breaks the Chow test (1960) can beemployed: splitting stops if the achieved reduction does notensure the chosen significance level. Eventually, in order tocircumvent the problem of model mispecification, in our programmevarious models can be assumed growing candidate trees (i.e., setsof breaks). The performance of the proposed approach is evaluatedby means of a simulation study. An application to the US laborproductivity index is also presented and discussed