### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 20-41 |

ページ数 | 22 |

ジャーナル | Journal of Econometrics |

巻 | 197 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 2017 3 1 |

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### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics
- History and Philosophy of Science

### これを引用

*Journal of Econometrics*,

*197*(1), 20-41. https://doi.org/10.1016/j.jeconom.2016.10.004

**Estimation of integrated quadratic covariation with endogenous sampling times.** / Potiron, Yoann; Mykland, Per A.

研究成果: Article

*Journal of Econometrics*, 巻. 197, 番号 1, pp. 20-41. https://doi.org/10.1016/j.jeconom.2016.10.004

}

TY - JOUR

T1 - Estimation of integrated quadratic covariation with endogenous sampling times

AU - Potiron, Yoann

AU - Mykland, Per A.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Asymptotic bias

KW - Asynchronous times

KW - Endogenous model

KW - Hayashi–Yoshida estimator

KW - High-frequency data

KW - Quadratic covariation

KW - Time endogeneity

UR - http://www.scopus.com/inward/record.url?scp=85007481039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007481039&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2016.10.004

DO - 10.1016/j.jeconom.2016.10.004

M3 - Article

AN - SCOPUS:85007481039

VL - 197

SP - 20

EP - 41

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -