On U- and V-statistics for discontinuous Ito semimartingales

Mark Podolskij, Christian Schmidt, Mathias Vetter

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Abstract

In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Itô semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated stable central limit theorems. In most of the cases the limiting process will be conditionally centered Gaussian. The structure of the kernel function determines whether the jump and/or the continuous part of the semimartingale contribute to the limit.

Original languageEnglish
JournalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
Volume53
Issue3
Pages (from-to)1007-1050
Number of pages44
ISSN0246-0203
DOIs
Publication statusPublished - Aug 2017

Keywords

  • High frequency data
  • Limit theorems
  • Semimartingales
  • Stable convergence
  • U-statistics

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