Comment on: Limit of Random Measures Associated with the Increments of a Brownian Semimartingale

Mark Podolskij and Mathieu Rosenbaum

Journal of Financial Econometrics, 2018, vol. 16, issue 4, 588-598

Abstract: 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.

Keywords: fractional Brownian motion; functional limit theorems; local times; quadratic variation (search for similar items in EconPapers)
Date: 2018
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