A segmentation approach to regression problems with switching-points

Regression problems with switching-points arise in many fields and has been recognized as a challenging issue for modern, big data applications. Many approaches to estimating switching regression models can only deal with continuous switching-point problem successfully. However, regression problems with jump discontinuities are often encountered in reality such as those in econometrics and engineering. This article presents a segmentation method for switching regression estimations, allowing for detecting both continuous and discontinuous switching-points. We consider using Taylor's expansion with an adjustment constant to derive the estimates of switching-points and regression parameters simultaneously. The proposed method can detect both jump-points and continuous switching-points. The proposed method is evaluated via experiments with numerical examples. The simulation results show the proposed method work well for both continuous and dis-continuous models and produce rather accurate estimates.