No. 972

Title:

Estimating correlations with nonsynchronous observations in continuous diffusion models

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 sampling, high-frequency data, nonsynchronicity, quadratic variation, realized volatility.

Abstract:

We consider the problem of estimating the covariance/correlation of two diffusion-type processes when they are observed only at discrete times in a nonsynchronous manner. In the preceding work, we proposed a new estimation procedure which is free of any `synchronization' processing of original data and yields consistent estimators for the true covariance/correlation of the processes as the observation interval shrinks to zero (in our 2003 paper, now Hayashi and Yoshida 2005), and established asymptotic normality for the covariance estimator (Hayashi and Yoshida 2004). This paper advances the theory further: (i) to establish joint asymptotic normality of the covariance estimator with the realized volatilities and, as its direct application; (ii) to show asymptotic normality of the correlation estimators constructed by the same principle when the true volatilities and correlation are constant. Three examples are discussed as an illustration of the usefulness of the theory.