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On estimation of quadratic variation for multivariate pure jump semimartingales | | Johannes Heiny
; Mark Podolskij
; | | Date: |
6 Sep 2020 | | Abstract: | In this paper we present the asymptotic analysis of the realised quadratic
variation for multivariate symmetric $eta$-stable Lévy processes, $eta
in (0,2)$, 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
$eta$-stable Lévy process when the original process is symmetric
$eta$-stable, while the limit is conditionally $eta$-stable in case of
integrals with respect to symmetric $eta$-stable motions. These asymptotic
results are mostly related to the work [5], 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 Lévy setting to obtain
confidence regions. | | Source: | arXiv, 2009.02786 | | Services: | Forum | Review | PDF | Favorites | |
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