Estimation of the quadratic variation of log prices based on the Itô semi-martingale

Abstract

As the availability of high-frequency data becomes more widespread, it has become very popular to model random fluctuations of some econometric variables over time using Itô semi-martingale. An emblematic problem is to estimate the quadratic variation, i.e., the integrated volatility of log prices, using noisy high frequency data with endogenous time and jumps. We propose a methodology that combines the multiple sub-grids and thresholds. First, the sub-sample is used to reduce the effect of the noise. Then, the threshold method is used to get rid of the effect of jumps. Finally, the multiple sub-grids method is used to increase the convergence rate. The asymptotic properties, such as consistency and asymptotic normality, are investigated. Simulation is also included to illustrate the performance of the proposed procedure.

Keywords

• multiple sub-grids
• threshold
• endogenous
• jumps
• semi-martingale