On the Performance of the Fluctuation Test for Structural Change

Abstract

We discuss the performance of “closed-end” fluctuation tests, used to detect changes in the structural stability of a model, in the case where the time horizon is large and the observations do not possess high enough moments. It is demonstrated via a simulation study that, in the latter case, the choice of the boundary function should take into account the number of moments existing; otherwise the actual size of the test may exceed the nominal level. We suggest an alternative “open-end” fluctuation procedure and study its asymptotic behavior. It turns out that if an improper boundary function is chosen, then the null hypothesis may be rejected even if it is true. This means that an appropriate choice of the boundary function requires some prior information about the tail heaviness of the observations. This is different from the cumulative sum-based monitoring schemes suggested by Chu et al. (1996) and further studied by Horváth et al. (2004).

Keywords:

• Approximate critical value
• Fluctuation test
• Heavy tail
• Low moment
• Monitoring procedure
• Sequential change point test
• Stopping time
• Structural break

Subject Classification:

• Primary 62L10
• Secondary 62G10
• 62G20
• 62G32

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support by NATO Grant PST.EAP.CLG 980599. The work of Lajos Horváth has also partially been supported by NSF Grant DMS 0604670 and Grant RGC-HKUST6428/06H.