Bootstrap tests for structural change with infinite variance observations

The quest of structural change with infinite variance observations appears to be relatively common. Conventional residual CUSUM of squares test (RCUSQ) are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a residual-based bootstrap approach to RCUSQ testing that is valid against a range of infinite variance processes. Our proposed method does not require the practitioners to specify knowledge for tailed index. Consistency and the rate of convergence for the estimated change point are also obtained. We also show via simulations that our asymptotic results provide good approximations in finite samples. In addition, we apply our results to investigate the original returns for NO.1 SDS using a historical data set that covers the period 1999–2002.