On non-standard limits of Brownian semi-stationary processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Gaertner, Kerstin¹  Podolskij, Mark² 

[1] Univ Vet Med, Inst Populat Genet, A-1210 Vienna, Austria

[2] Univ Aarhus, Dept Math, DK-8000 Aarhus C, Denmark

关键词: Brownian semi-stationary processes;    High frequency data;    Limit theorems;    Stable convergence;   

DOI  :  10.1016/j.spa.2014.09.019

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free