Limit theorems for non-degenerate U-statistics of continuous semimartingales

Mark Podolskij (), Christian Schmidt () and Johanna Fasciati Ziegel ()
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Mark Podolskij: Heidelberg University and CREATES, Postal: Department of Mathematics, 69120 Heidelberg, Germany
Christian Schmidt: Heidelberg University, Postal: Department of Mathematics, 69120 Heidelberg, Germany
Johanna Fasciati Ziegel: University of Bern, Postal: Department of Mathematics and Statistics, Institute of Mathematical Statistics and Actuarial Science, Sidlerstrasse 5, 3012 Bern, Switzerland

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Keywords: High frequency data; Limit theorems; Semimartingales; Stable convergence; U-statistics (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 30
Date: 2012-10-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
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