M-procedures for detection of a change under weak dependence

•CUSUM procedures for robust change point detection in regression are considered.•We allow for the weak dependence in the regressors and errors.•Lp-m approximability and M-estimators are used in asymptotic analysis.

Procedures detecting a change of regression parameters in a linear model are considered when both the regressors and the errors are weakly dependent in the sense of Lp–m-approximability. M-estimators and weighted M-residuals are used to construct test statistics, and their asymptotic distribution is studied under the null hypothesis of no change and under contiguous alternatives. Estimators of a long-run variance are also considered and studied both analytically and numerically.