When estimating integrated covariationbetween two assets based on high-frequency data , simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional modeland show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes .
When estimating high-frequency covariance (quadratic covariation) of two arbitrary assets observed asynchronously , simple assumptions are usually imposed on the relationship between the prices process and the observation times. In this paper, we introduce a very general endogenous two dimensional nonparametric model. Because an observation is generated whenever an auxiliary process called observation time process hits one of the two boundary processes, it is called the hitting boundary process with time process (HBT) model. We establish a central limit theorem for the Hayashi-Yoshida estimator under HBT in the case where prices process follows a continuous Ito process: we obtain an asymptotic bias. We provide an estimator of the latter as well as a bias-corrected estimator of the high-frequency covariance. In addition, we give a consistent estimator of the associated standard error .
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integrated covariationbetween two assets based on
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data
covariance (quadratic covariation) of two arbitrary assets observed asynchronously
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price processes
prices process
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an endogenous 2-dimensional modeland show that it is more general than the existing endogenous models of the literature. In addition, we
a very general endogenous two dimensional nonparametric model. Because an observation is generated whenever an auxiliary process called observation time process hits one of the two boundary processes, it is called the hitting boundary process with time process (HBT) model. We
R
in this general endogenous model in
under HBT in
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follow pure-diffusion processes
process follows a continuous Ito process: we obtain an asymptotic bias. We provide an estimator of the latter as well as a bias-corrected estimator of the high-frequency covariance. In addition, we give a consistent estimator of the associated standard error