Real time change-point detection in a model by adaptive LASSO and CUSUM

In this paper, the CUSUM test statistic based on adaptive LASSO residuals is proposed and studied for detecting in real time a change-point in a linear model with a large number of explanatory variables. 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 infinity. These results allow to build an asymptotic critical region. Next, in order to improve the test statistic performance a modified test statistic is proposed. Simulation results, using Monte Carlo technique, illustrate the performance of the proposed test statistic. We also compare it with the classical CUSUM test statistic.