No. 971

Title:

Asymptotic normality of nonsynchronous covariance estimators for diffusion processes

Author(s):

HAYASHI, Takaki (Keio University, Graduate School of Business Administration);
YOSHIDA, Nakahiro (University of Tokyo, Graduate School of Mathematical Sciences);

Key words:

diffusions, discrete-time observations, high-frequency data, nonsynchronicity, quadratic variation, realized volatility.

Abstract:

We consider the problem of estimating the covariance of two diffusion-type processes when they are observed only at discrete times in a nonsynchronous manner. In our previous work in 2003, we proposed a new estimator which is free of any `synchronization' processing of the original data and showed that it is consistent for the true covariance of the processes as the observation interval shrinks to zero (Hayashi and Yoshida 2005). This paper advances the new theory further. Specifically, it establishes asymptotic normality of the estimator in a general nonsynchronous sampling scheme.