Multiple Change-Point Detection in Linear Regression Models via U-Statistic Type Processes

Many procedures have been developed that are suited to testing for multiple changes in parameters of regression models which occur at unknown times. Most notably, Brown, Durbin and Evans [11] and Dufour [15], have developed or extended existing techniques, but said extensions lack power for detecting changes (cf. Kramer, Ploberger, Alt [24] and Pouliot [32] in the intercept parameter of linear regression models. Orasch [26] has developed a stochastic process that easily accommodates testing for many change-points that occur at unknown times. A slight modification of his process is suggested here which improves the power of statistics fashioned from it. These statistics are then used to construct tests to detect multiple changes in intercept in linear regression models. It is also shown here that this slightly altered process, when weighted by appropriately chosen functions, is sensitive to detection of multiple changes in intercept that occur both early and later on in the sample, while maintaining sensitivity to changes that occur in the middle of the sample.