Bernoulli

  • Bernoulli
  • Volume 25, Number 3 (2019), 2245-2278.

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

Andrea Granelli and 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.

Article information

Source
Bernoulli, Volume 25, Number 3 (2019), 2245-2278.

Dates
Received: August 2017
Revised: June 2018
First available in Project Euclid: 12 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1560326444

Digital Object Identifier
doi:10.3150/18-BEJ1052

Mathematical Reviews number (MathSciNet)
MR3961247

Zentralblatt MATH identifier
07066256

Keywords
bivariate Brownian semistationary process central limit theorem fourth moment theorem high frequency data moving average process multivariate setting stable convergence

Citation

Granelli, Andrea; Veraart, Almut E.D. A central limit theorem for the realised covariation of a bivariate Brownian semistationary process. Bernoulli 25 (2019), no. 3, 2245--2278. doi:10.3150/18-BEJ1052. https://projecteuclid.org/euclid.bj/1560326444


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Supplemental materials

  • Supplement to “A central limit theorem for the realised covariation of a bivariate Brownian semistationary process”. We collect technical details and proofs in the supplementary article, which should be read in conjunction with the present paper.