Pointwise Hurst Estimation via Scale Accumulation: A Noise-Robust Approach for Rough Volatility
通过尺度累积逐点估计 Hurst 参数:粗糙波动率的抗噪方法
We introduce an estimator for the pointwise, time-varying Hölder exponent (Hurst parameter) of a stochastic process, based on the geometry accumulation integral G_Lambda(t) = integral from Lambda to 1 of |eth_s X(t)| s^{-1} ds, where eth_s X(t) = (X(t+s)-X(t))/s is the scale derivative at resolution s. We prove consistency, noise robustness with explicit threshold Lambda* = sigma^{1/H}, and a CLT at rate (log Lambda)^{-1/2}. The estimator is pointwise in time, defined at…