Abstract
We consider the problem of estimating volatility for high-frequency data when the observed process is the sum of a continuous Ito semimartingale and a noise process that locally behaves like fractional Brownian motion with Hurst parameter H. The resulting class of processes, which we call mixed semimartingales, generalizes the mixed fractional Brownian motion introduced by Cheridito [Bernoulli 7 (2001) 913–934] to time-dependent and stochastic volatility. Based on central limit theorems for variation functionals, we derive consistent estimators and asymptotic confidence intervals for H and the integrated volatilities of both the semimartingale and the noise part, in all cases where these quantities are identifiable. When applied to recent stock price data, we find strong empirical evidence for the presence of fractional noise, with Hurst parameters H that vary considerably over time and between assets.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
