Limit theorems for the pre-averaged Hayashi-Yoshida estimator with random sampling

作者：Koike Yuta^*

来源：Stochastic Processes and Their Applications, 2014, 124(8): 2699-2753.

DOI：10.1016/j.spa.2014.03.008

• Hayashi-Yoshida estimator
• Integrated covariance
• Market microstructure noise
• Nonsynchronous observations
• Pre-averaging
• Stable convergence
• Strong predictability

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.

• 出版日期2014-8