On non-standard limits of Brownian semi-stationary

Kerstin Gärtner () and Mark Podolskij ()
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Kerstin Gärtner: Vienna University, Postal: Institute of Population Genetics, University of Veterinary Medicine, Veterinärplatz 1, 1210 Vienna, Austria
Mark Podolskij: Aarhus University and CREATES, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark

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

Abstract: In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary (BSS) processes. More precisely, we will show that singularities in the weight function, which is one of the ingredients of a BSS process, may lead to non-standard limits of the realised quadratic variation. In this case the limiting process is a convex combination of shifted integrals of the intermittency function. Furthermore, we will demonstrate the corresponding stable central limit theorem. Finally, we apply the probabilistic theory to study the asymptotic properties of the realized ratio statistics, which estimates the smoothness parameter of a BSS process.

Keywords: Brownian semi-stationary processes; high frequency data; limit theorems; stable convergence (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 28
Date: 2014-12-10
New Economics Papers: this item is included in nep-ecm and nep-ets
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