Nonparametric estimation of structural breakpoints

Abstract

This paper proposes point and interval estimates of location and size of jumps in multiple regression curves or its derivatives. We are mainly concerned with time series models where structural breaks occur at a given period of time or they are explained by the value taken by some predictor (e.g. threshold models). No previous knowledge of the underlying regression function is required. Left and right limits of the function, with respect to the regressor explaining the break, are estimated at each data point using multivariate multiplicative kernels. The univariate kernel corresponding to the regressor explaining the break is one-sided, with all its mass at the right or left of zero. Since left and right limits are the same, except at the break point, the location of the jump is estimated as the observed regressor value maximizing the difference between left and right limit estimates. This difference, evaluated at the estimated location point, is the estimation of the jump size. A small Monte Carlo study and an empirical application to USA macroecomic data illustrates the performance of the procedure in small samples. The paper also discusses some extensions, in particular the identification of the coordinate explaining the break, the application of the procedure to the estimation of parametric models, and robustification of the method for the influence of outliers.