On non-standard limits of Brownian semi-stationary processes

TY - JOUR

T1 - On non-standard limits of Brownian semi-stationary processes

AU - Gärtner, Kerstin

AU - Podolskij, Mark

PY - 2015

Y1 - 2015

N2 - In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary 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.

AB - In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary 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.

KW - math.PR

KW - 60F05, 60F15, 60F17

U2 - 10.1016/j.spa.2014.09.019

DO - 10.1016/j.spa.2014.09.019

M3 - Journal article

SN - 0304-4149

VL - 125

SP - 653

EP - 677

JO - Stochastic Processes and Their Applications

JF - Stochastic Processes and Their Applications

IS - 2

ER -