Department Seminar by Xiyue Han

Please Note: This seminar will be given online.

The Hurst roughness exponent and its model-free estimation

We introduce the concept of the Hurst roughness exponent $H_r$ as a generalization of the Hurst parameter to arbitrary continuous functions. The Hurst roughness exponent characterizes the regularity of a function in the following sense; a function admitting the Hurst roughness exponent $H_r$ has vanishing $p^{th}$ variation for all $p > 1/H_r$ and infinite $p^{th}$ variation for $p < 1/H_r$. Moreover, we provide a class of model-free consistent estimators for the Hurst roughness exponent under simple assumptions. These estimators are model-free in the sense that they do not require any probabilistic assumptions and work with single time series. As an application, we apply our estimators to measure the roughness of realized volatility processes of various financial indices.