Monitoring persistence change in infinite variance observations

In this paper, we adopt a kernel-weighted variance ratio statistic to monitor persistence change in infinite variance observations. We focus on a I(0) to I(1) regime switch for sequences in the domain of attraction of a stable law and local-to-finite variance sequences. The null distribution of the monitoring statistic and its consistency under alternative hypothesis are proved. In particular, a bootstrap approximation is proposed to determine the critical values for the derived asymptotic distribution depends on the unknown tail index. The small sample performance of the proposed monitoring procedures are illustrated by both simulation and application to Sweden/US foreign exchange rate data.