A new procedure for unit root to long-memory process change-point monitoring

In this paper, we propose a Dickey-Fuller difference statistic to sequentially detect the change-point that shift from an unit root process to a long-memory process. The limiting distribution of monitoring statistic under the unit root process null hypothesis as well as its consistency under the alternative hypothesis are proved. Simulations indicate that the new method can control the empirical size well even for the heavy-tailed unit root …