A central limit theorem for the realised covariation of a bivariate Brownian semistationary process

Andrea Granelli, Almut E.D. Veraart

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Abstract

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus.

Original languageEnglish
JournalBernoulli
Volume25
Issue3
Pages (from-to)2245-2278
Number of pages34
ISSN1350-7265
DOIs
Publication statusPublished - 1 Jan 2019
Externally publishedYes

Keywords

  • Bivariate Brownian semistationary process
  • Central limit theorem
  • Fourth moment theorem
  • High frequency data
  • Moving average process
  • Multivariate setting
  • Stable convergence

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