Faster Convergence to the Estimation of Quadratic Variation with Microstructure Noise

Abstract

The continuous quadratic variation of asset return plays a critical role for high-frequency trading. However, the microstructure noise could bias the estimation of the continuous quadratic variation. Zhang et al. (2005) proposed a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This article proposes a recursive version of their estimator that outputs variation estimates as the data arrive. Our estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of the recursive estimator.

Keywords:

• Quadratic variation
• Realized variation
• High-frequency
• Microstructure noise

Mathematics Subject Classification:

• 37M10