A CUSUM Tests for Stable Index Changes under Heavy-Tailed Sequences

Based on the CUSUM test, this paper considers testing a heavy index break of heavy-tailed observations with infinite variance. Given for the appropriate conditions, the asymptotic distribution of the test statistic is obtained under the null hypothesis and its consistency is proved under the alternative hypothesis. The critical value can be obtained by Monte Carlo simulation and its respond curve is obtained by fitting. Finally, a Monte Carlo study shows that our test has reasonably good size and power properties in finite samples.