On estimation of quadratic variation for multivariate pure jump semimartingales

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:138

Article

Heiny, Johannes¹  Podolskij, Mark^2,3 

[1] Ruhr Univ Bochum, Dept Math, Bochum, Germany

[2] Univ Luxembourg, Dept Math, Luxembourg, Luxembourg

[3] Univ Luxembourg, Dept Finance, Luxembourg, Luxembourg

关键词: High frequency data;    Levy processes;    Limit theorems;    Quadratic variation;    Semimartingales;   

DOI  :  10.1016/j.spa.2021.04.016

来源: Elsevier

【 摘 要 】

In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric beta-stable Levy processes, beta is an element of (0, 2), and certain pure jump semimartingales. The main focus is on derivation of functional limit theorems for the realised quadratic variation and its spectrum. We will show that the limiting process is a matrix-valued beta-stable Levy process when the original process is symmetric beta-stable, while the limit is conditionally beta-stable in case of integrals with respect to locally beta-stable motions. These asymptotic results are mostly related to the work (Diop et al., 2013), which investigates the univariate version of the problem. Furthermore, we will show the implications for estimation of eigenvalues and eigenvectors of the quadratic variation matrix, which is a useful result for the principle component analysis. Finally, we propose a consistent subsampling procedure in the Levy setting to obtain confidence regions. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free