Nonparametric inference for spot volatility in pure-jump semimartingales

Chengxin Yan; Dachuan Chen; Jia Li

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arXiv · 2601.18371

Nonparametric inference for spot volatility in pure-jump semimartingales

Chengxin Yan·Dachuan Chen·Jia Li

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Abstract

We provide a comprehensive analysis of spot volatility inference in pure-jump semimartingales under two asymptotic settings: fixed-$k$, where each local window uses a fixed number of observations, and large-$k$, where this number grows with sampling frequency. For both active- and possibly inactive-jump settings, we derive generally nonstandard, typically non-Gaussian limit distributions and establish valid inference, including when the jump-activity index is consistently estimated. Simulations show that fixed-$k$ asymptotics offer markedly better finite-sample accuracy, underscoring their practical advantage for nonparametric spot volatility inference.

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Chengxin Yan, Dachuan Chen, Jia Li. 2026-01-26. Nonparametric inference for spot volatility in pure-jump semimartingales. https://arxiv.org/abs/2601.18371

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