Two tests for sequential detection of a change-point in a nonlinear model

TL;DR

This paper introduces two sequential change-point detection tests for nonlinear models, extending existing methods from linear models, with theoretical analysis and simulation validation for real-time applications.

Contribution

It proposes a novel extension of CUSUM-based and least squares tests for nonlinear models, including asymptotic distributions and bootstrap methods for improved accuracy.

Findings

Asymptotic distribution under null hypothesis established

Bootstrap critical values reduce type I error

Simulation confirms effectiveness in nonlinear models

Abstract

In this paper, two tests, based on CUSUM of the residuals and least squares estimation, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the literature but for the linear models. It is tested the null hypothesis, at each sequential observation, that there is no change in the model against a change presence. The asymptotic distribution of the test statistic under the null hypothesis is given and its convergence in probability to infinity is proved when a change occurs. These results will allow to build an asymptotic critical region. Next, in order to decrease the type I error probability, a bootstrapped critical value is proposed and a modified test is studied in a similar way. Simulation results, using Monte-Carlo technique, for nonlinear models which have numerous applications, investigate the properties of the two statistic tests.