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arXiv · 2606.25771

Pointwise Hurst Estimation via Scale Accumulation: A Noise-Robust Approach for Rough Volatility

Jokubas Petkevicius
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Abstract

We introduce an estimator for the pointwise, time-varying H\"older 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 finite resolution, and eliminates microstructure noise by scale separation. Existing estimators give a global H from integrated variance; this gives a time-varying H(t) directly from the price path.

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Jokubas Petkevicius. 2026-06-24. Pointwise Hurst Estimation via Scale Accumulation: A Noise-Robust Approach for Rough Volatility. https://arxiv.org/abs/2606.25771

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