Bayesian estimation of the Hurst parameter of fractional Brownian motion

摘要

The primary purpose of this study was to find Bayesian estimates for the Hurst dimension of a Fractional Brownian motion with a Beta prior when the process is observed at discrete times. Overestimation is observed though the overestimation is less severe as real H goes up. In addition, the estimated H decreases as Beta parameters go up given an Alpha value. In contrast, the estimated H increases as Alpha parameters go up given a Beta value. For the real-world data, the 2011 daily Taiwan stock index was used and the estimated Hurst index was 0.21.