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Estimation of integrated quadratic covariation with endogenous sampling times

Yoann Potiron () and Per A. Mykland

Journal of Econometrics, 2017, vol. 197, issue 1, 20-41

Abstract: When estimating high-frequency covariance (quadratic covariation) of two arbitrary assets observed asynchronously, simple assumptions, such as independence, are usually imposed on the relationship between the prices process and the observation times. In this paper, we introduce a 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 (HY) estimator under HBT in the case where the price process and the observation price process follow a continuous Itô process. We obtain an asymptotic bias. We provide an estimator of the latter as well as a bias-corrected HY estimator of the high-frequency covariance. In addition, we give a consistent estimator of the associated standard error.

Keywords: Asymptotic bias; Asynchronous times; Endogenous model; Hayashi–Yoshida estimator; High-frequency data; Quadratic covariation; Time endogeneity (search for similar items in EconPapers)
JEL-codes: C01 C02 C13 C14 C22 C32 C58 (search for similar items in EconPapers)
Date: 2017
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