Real time change-point detection in a nonlinear quantile model

Most studies in real-time change-point detection either focus on the linear model or use the cumulative sum (CUSUM) method under classical assumptions on model errors. This article considers the sequential change-point detection in a nonlinear quantile model. A test statistic based on the CUSUM of the quantile process subgradient is proposed and studied. Under the null hypothesis that the model does not change, the asymptotic distribution of the test statistic is determined. Under the alternative hypothesis that at some unknown observation there is a change in the model, the proposed test statistic converges in probability to . These results allow building the critical regions on open-end and on closed-end procedures. Simulation results, using a Monte Carlo technique, investigate the performance of the test statistic, especially for heavy-tailed error distributions. We also compare it with the classical CUSUM test statistic. An example on real data is also given.