Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes |
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Authors: | Takaki Hayashi Nakahiro Yoshida |
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Affiliation: | (1) Keio University, Graduate School of Business Adminstration, 2-1-1 Hiyoshi-honcho, Yokohama 223-8523, Japan;(2) The University of Tokyo, Graduate School of Mathematical Sciences, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan |
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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 (Bernoulli, 11, 359–379, 2005). This paper is its sequel. Specifically, it establishes asymptotic normality of the estimator in a general nonsynchronous sampling scheme. |
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Keywords: | Diffusions Discrete-time observations High-frequency data Nonsynchronicity Quadratic variation Realized volatility |
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