A weak law of large numbers for realised covariation in a Hilbert space setting

Fred Espen Benth, Dennis Schroers and Almut Veraart

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 241-268

Abstract: This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated volatility process arising in general mild solutions of Hilbert space-valued stochastic evolution equations in the sense of Da Prato and Zabczyk (2014). We prove a weak law of large numbers for this estimator, where the convergence is uniform on compacts in probability with respect to the Hilbert–Schmidt norm. In addition, we determine convergence rates for common stochastic volatility models in Hilbert spaces.

Keywords: Law of large numbers; High-frequency estimation; Quadratic covariation; Volatility; Hilbert space; Evolution equations (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:145:y:2022:i:c:p:241-268

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DOI: 10.1016/j.spa.2021.12.011

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