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A feasible central limit theorem for realised covariation of SPDEs in the context of functional data

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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



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