On non-standard limits of Brownian semi-stationary processes

Kerstin Gärtner and Mark Podolskij

Stochastic Processes and their Applications, 2015, vol. 125, issue 2, 653-677

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 realised 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)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:2:p:653-677

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DOI: 10.1016/j.spa.2014.09.019

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