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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.18371 |
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| _version_ | 1866911399363477504 |
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| author | Yan, Chengxin Chen, Dachuan Li, Jia |
| author_facet | Yan, Chengxin Chen, Dachuan Li, Jia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonparametric inference for spot volatility in pure-jump semimartingales Yan, Chengxin Chen, Dachuan Li, Jia Statistics Theory 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. |
| title | Nonparametric inference for spot volatility in pure-jump semimartingales |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2601.18371 |