• Corpus ID: 248571524

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

@inproceedings{Benth2022AFC,
  title={A feasible central limit theorem for realised covariation of SPDEs in the context of functional data},
  author={Fred Espen Benth and Dennis Schroers and Almut E. D. Veraart},
  year={2022}
}

• F. Benth, Dennis Schroers, Almut E. D. Veraart
• Published 8 May 2022
• Mathematics

. 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.