<p>This study addresses the problem of online change-point detection in time-dependent linear regression models that incorporate autoregressive terms in both the response variable and the residuals. We refer to this framework as the dynamic regression model with autoregressive residuals (DREGAR). We propose a vector-valued CUSUM statistic based on the adaptive LASSO (ALASSO) algorithm to detect coefficient changes in the DREGAR model. For the proposed statistic, we establish its asymptotic distribution under the null hypothesis and demonstrate its divergence under the alternative hypotheses. Through simulations, we show that our method significantly outperforms classical CUSUM-based methods in terms of detection powers and mean detection delay. Furthermore, it exhibits superior performance compared to the existing recursive residual based vector-valued CUSUM method. Finally, the practical utility of the proposed method is demonstrated through empirical studies on long-term residential electricity consumption data and international financial markets.</p>