Comment on: Limit of Random Measures Associated with the Increments of a Brownian Semimartingale: Asymptotic behavior of local times related statistics for fractional Brownian motion

TY - JOUR

T1 - Comment on: Limit of Random Measures Associated with the Increments of a Brownian Semimartingale: Asymptotic behavior of local times related statistics for fractional Brownian motion

AU - Podolskij, Mark

AU - Rosenbaum, Mathieu

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We consider high-frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of various classical statistics related to the local times of the process. We show that as in the diffusion case, these statistics indeed converge to some local times up to a constant factor. As a corollary, we provide limit theorems for the quadratic variation of the absolute value of a fractional Brownian motion.

AB - We consider high-frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of various classical statistics related to the local times of the process. We show that as in the diffusion case, these statistics indeed converge to some local times up to a constant factor. As a corollary, we provide limit theorems for the quadratic variation of the absolute value of a fractional Brownian motion.

KW - Fractional Brownian motion

KW - Functional limit theorems

KW - Local times

KW - Quadratic variation

UR - https://www.scopus.com/pages/publications/85055494756

U2 - 10.1093/jjfinec/nbx036

DO - 10.1093/jjfinec/nbx036

M3 - Journal article

SN - 1479-8409

VL - 16

SP - 588

EP - 598

JO - Journal of Financial Econometrics

JF - Journal of Financial Econometrics

IS - 4

ER -