Variance change point detection for fractional Brownian motion based on the likelihood ratio test

Abstract

Fractional Brownian motion is one of the main stochastic processes used for describing the long-range dependence phenomenon for self-similar processes. It appears that for many real time series, characteristics of the data change significantly over time. Such behaviour one can observe in many applications, including physical and biological experiments. In this paper, we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional Brownian motion with a time-changed diffusion coefficient. The proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for Brownian motion, the process with independent increments. Here, we also propose a statistical test for testing the significance of the estimated critical point. In addition to that, an extensive simulation study is provided to test the performance of the proposed method.