Quadratic Variation Estimation of an Irregularly Observed Semimartingale with Jumps and Noise

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Yuta Koike*
• Keywords: jumps ; microstructure noise ; volatility ; stochastic process ; asymptotic theory

Abstract

The estimation of the quadratic variation of a semimartingale observed at a high-frequency is considered. High-frequency financial data are often modeled by discrete observations of a semimartingale, and the quadratic variation can be seen as a measure of the volatility of the corresponding asset, so its estimation has attracted attention in financial econometrics recently. In this talk, the situation where the observation data are contaminated by microstructure noise and the observed semimartingale is allowed to have jumps is considered, and the estimation of the entire quadratic variation is discussed. In such a situation, a pre-averaged version of the realized variance estimator is considered as a natural estimator for the quadratic variation. This talk presents the asymptotic mixed normality of this estimator under the situation where the observation times show irregularity. In particular, the result shows that some standard methods for constructing confidence intervals of the estimator, which are derived under the regular sampling assumption, are still valid in many irregular sampling settings.