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 Chu , C. S. J. , Stinchcombe , M. and White , H. ( 1996 ). Monitoring Structural Change , Econometrica 64 : 1045 – 1065 .Crossref], Web of Science ®] , Google Scholar]) and further studied by Horváth et al. (2004 Horváth , L. , Hu?ková , M. , Kokoszka , P. , and Steinebach , J. ( 2004 ). Monitoring Changes in Linear Models , Journal of Statistical Planning and Inference 126 : 225 – 251 .Crossref], Web of Science ®] , Google Scholar]).