Monitoring Change in Persistence Against the Null of Difference-Stationarity in Infinite Variance Observations

Abstract

In this article, we propose a moving kernel-weighted variance ratio statistic to monitor persistence change in infinite variance observations. We focus on I (1) to I (0) persistence change 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 are proved. In particular, a bootstrap procedure is proposed to determine the critical values for the derived asymptotic distribution depends on unknown tail index. The small sample performances of proposed monitoring procedure are illustrated by both simulation and application to a high frequency financial data.