On estimation of quadratic variation for multivariate pure jump semimartingales

Johannes Heiny and Mark Podolskij

Stochastic Processes and their Applications, 2021, vol. 138, issue C, 234-254

Abstract: In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric β-stable Lévy processes, β∈(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 β-stable Lévy process when the original process is symmetric β-stable, while the limit is conditionally β-stable in case of integrals with respect to locally β-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 Lévy setting to obtain confidence regions.

Keywords: High frequency data; Lévy processes; Limit theorems; Quadratic variation; Semimartingales (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.04.016

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