Semi-parametric tests to sequential detection of a change-point in a nonlinear model

In this paper, two semi-parametric tests, based on CUSUM errors and least squares estimation, are studied to detect in real time a change-point in a nonlinear model. Test statistic is found to test, for each sequential observation, that there is no change in the model against a change presence. A bootstrapped critical value is proposed for decrease the type I error probability. Simulation results, using Monte-Carlo technique, for nonlinear models which have numerous applications, support the relevance of the theory.