Sequential monitoring change in persistence of polynomial regression model

This article considers a sequential monitoring procedure designed to detect a change from I(1) to I(0) in a polynomial regression model. A modified kernel-weighted variance ratio statistic based on updated residual was proposed to detect the persistent change more quickly and more powerfully. The null distribution of the monitoring statistic and its consistency under alternative hypothesis were proved. Simulations indicated that our procedure achieved a good performance on finite sample for early change and late change.