Limit theorems for the realised semicovariances of multivariate
Brownian semistationary processes
Brownian semistationary processes
File(s)
Published version
Author(s)
Li, Yuan
Pakkanen, Mikko
Veraart, Almut
Type
Journal Article
Abstract
In this article, we will introduce the realised semicovariance for Brownian semistationary (BSS) processes, which is obtained from the decomposition of the realised covariance matrix into components based on the signs of the returns and study its in-fill asymptotic properties. More precisely, weak convergence in the space of càdlàg functions endowed with the Skorohod topology for the realised semicovariance of a general Gaussian process with stationary increments is proved first. The proof is based on the Breuer–Major theorem and on a moment bound for sums of products of non-linearly transformed Gaussian vectors. Furthermore, we establish a corresponding stable convergence. Finally, a central limit theorem for the realised semicovariance of multivariate BSS processes is established. These results extend the limit theorems for the realised covariation to a result for non-linear functionals.
Date Issued
2023-01-01
Date Acceptance
2022-10-04
Citation
Stochastic Processes and their Applications, 2023, 155, pp.202-231
ISSN
0304-4149
Publisher
Elsevier
Start Page
202
End Page
231
Journal / Book Title
Stochastic Processes and their Applications
Volume
155
Copyright Statement
© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
(http://creativecommons.org/licenses/by/4.0/).
License URL
Subjects
math.PR
math.PR
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance and Investment
Statistics & Probability
Publication Status
Published
Date Publish Online
2022-10-13