A new limit result in change point analysis

Abstract

Change points are abrupt changes in time ordered data. The cumulative sum (CUSUM) test statistic is an important statistic for testing for a change point. In this article, we prove a functional central limit theorem for heterogeneous α-mixing triangular array in $D[0,1]$ assuming a Riemann integrable variance function. We investigate the asymptotic behavior of the CUSUM statistic under the null and alternative hypotheses through a simulation.

Keywords:

• α-Mixing
• functional central limit theorem
• triangular array