A test for change points under the roughness of stochastic volatility: the case of the VIX index

Abstract

ABSTRACT In light of the recent empirical studies with high-frequency data, the logarithm of the stock market volatility data behaves as a fractional Brownian motion (fBm) with the Hurst exponent smaller than 0.5. It thus leads to extensive research in the so-called rough volatility (RV). This paper introduces a novel non-parametric test for its change points detection problem, which combines the proposed autoregressive rough volatility (ARRV) model and an increment ratio (IR)-based filtering function. The empirical results of the VIX index show that our method can detect more accurate change points without dependence on initial conditions/parameters, work efficiently for trends and forecast robustly better.