Real time change-point detection in a nonlinear quantile model

TL;DR

This paper introduces a new sequential change-point detection method for nonlinear quantile models using a CUSUM-based statistic, effective under heavy-tailed errors, and compares it with classical methods.

Contribution

It proposes a novel CUSUM-based test statistic for change-point detection in nonlinear quantile models, extending beyond linear assumptions and classical error conditions.

Findings

The test statistic's asymptotic distribution under null hypothesis is derived.

The statistic diverges under the alternative hypothesis, indicating change detection.

Simulation results show improved performance with heavy-tailed errors compared to classical CUSUM.

Abstract

Most studies in real time change-point detection either focus on the linear model or use the CUSUM method under classical assumptions on model errors. This paper 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 null hypothesis that the model does not change, the asymptotic distribution of the test statistic is determined. Under alternative hypothesis that at some unknown observation there is a change in model, the proposed test statistic converges in probability to $\infty$. These results allow to build the critical regions on open-end and on closed-end procedures. Simulation results, using Monte Carlo technique, investigate the performance of the test statistic, specially for heavy-tailed error distributions. We also compare it with the classical CUSUM test statistic.