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A feasible central limit theorem for realised covariation of SPDEs in the context of functional data
File | Description | Size | Format | |
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SARCV_CLT.pdf | Accepted version | 634.61 kB | Adobe PDF | View/Open |
Title: | A feasible central limit theorem for realised covariation of SPDEs in the context of functional data |
Authors: | Benth, FE Schroers, D Veraart, A |
Item Type: | Journal Article |
Abstract: | This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup-adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup-adjusted multipower variations (SAMPV) and establish their weak law of large numbers; using SAMPV, we construct a consistent estimator of the asymptotic covariance of the mixed-Gaussian limiting process appearing in the central limit theorem for the SARCV, resulting in a feasible asymptotic theory. Finally, we outline how our results can be applied even if observations are only available on a discrete space-time grid. |
Issue Date: | 1-Apr-2024 |
Date of Acceptance: | 10-Sep-2023 |
URI: | http://hdl.handle.net/10044/1/107070 |
DOI: | 10.1214/23-AAP2019 |
ISSN: | 1050-5164 |
Publisher: | Institute of Mathematical Statistics |
Start Page: | 2208 |
End Page: | 2242 |
Journal / Book Title: | Annals of Applied Probability |
Volume: | 34 |
Issue: | 2 |
Copyright Statement: | © 2024 Institute of Mathematical Statistics. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising. |
Publication Status: | Published |
Appears in Collections: | Statistics Faculty of Natural Sciences Mathematics |
This item is licensed under a Creative Commons License