Strong consistency properties of the variance change point estimator based on strong-mixing samples

Abstract

In this paper, our primary attention was centered on the issue of detecting the variance change point for strong-mixing samples. We delved into the cumulative sum (CUSUM) estimator of variance change model and established the strong convergence rate of the variance change point estimation. Furthermore, to corroborate the effectiveness of the CUSUM based methodology, we have conducted a series of simulations, the outcomes of which underscored its validity.

Keywords

• variance change point
• cusum
• strong-mixing sequence
• strong consistency