An Advanced Segmentation Approach to Piecewise Regression Models

Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous models. Such a restriction really limits the practical applications of SEG when it comes to discontinuous jumps encountered in real change-point problems very often. In this paper, we propose a piecewise regression model, allowing for discontinuous jumps, connected lines, or the occurrences of jumps and connected change-points in a single model. The proposed segmentation approach can derive the estimates of jump points, connected change-points, and regression parameters simultaneously, allowing for multiple change-points. The initializations of the proposed algorithm and the decision on the number of segments are discussed. Experimental results and comparisons demonstrate the effectiveness and superiority of the proposed method. Several real examples from diverse areas illustrate the practicability of the new method.