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 language | English |
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Journal | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques |
Volume | 53 |
Issue | 3 |
Pages (from-to) | 1007-1050 |
Number of pages | 44 |
ISSN | 0246-0203 |
DOIs | |
Publication status | Published - Aug 2017 |
Keywords
- High frequency data
- Limit theorems
- Semimartingales
- Stable convergence
- U-statistics