Nonparametric Change Point Detection in Regression

This paper considers an important problem of change-point detection in regression. The study suggests a novel testing procedure featuring a fully data-driven calibration scheme. The method is essentially a black box, requiring no tuning from practitioner. We investigate the approach from both theoretical and practical point of view. The theoretical study demonstrates proper control of first-type error rate under $\mathbb{H}_0$ and power approaching $1$ under $\mathbb{H}_1$. We also conduct experiments on synthetic data fully supporting the theoretical claims. In conclusion we apply the method to financial data, where it detects sensible change-points. Techniques for change-point localization are also suggested and investigated.