Imperial College London
Alternate

ProfessorAlmutVeraart

Faculty of Natural Sciences, Department of Mathematics

Head of the Statistics Section, Professor of Statistics
 
 
 
//

Contact

 

+44 (0)20 7594 8545a.veraart Website

 
 
//

Location

 

551Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Li:2023:10.1016/j.spa.2022.10.001,
author = {Li, Y and Pakkanen, M and Veraart, A},
doi = {10.1016/j.spa.2022.10.001},
journal = {Stochastic Processes and their Applications},
pages = {202--231},
title = {Limit theorems for the realised semicovariances of multivariateBrownian semistationary processes},
url = {http://dx.doi.org/10.1016/j.spa.2022.10.001},
volume = {155},
year = {2023}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Li,Y
AU  - Pakkanen,M
AU  - Veraart,A
DO  - 10.1016/j.spa.2022.10.001
EP  - 231
PY  - 2023///
SN  - 0304-4149
SP  - 202
TI  - Limit theorems for the realised semicovariances of multivariateBrownian semistationary processes
T2  - Stochastic Processes and their Applications
UR  - http://dx.doi.org/10.1016/j.spa.2022.10.001
UR  - http://hdl.handle.net/10044/1/100385
VL  - 155
ER  -
Download