### 抜粋

An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and themselves. The nonsynchronous covariation process converges to the usual quadratic covariation of the semimartingales as the maximum size of the sampling intervals tends to zero. We deal with the case where the limiting variation process of the normalized approximation error is random and prove the convergence to mixed normality, or convergence to a conditional Gaussian martingale. A class of consistent estimators for the asymptotic variation process based on kernels is proposed, which will be useful for statistical applications to high-frequency data analysis in finance. As an illustrative example, a Poisson sampling scheme with random change point is discussed.

元の言語 | English |
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ページ（範囲） | 2416-2454 |

ページ数 | 39 |

ジャーナル | Stochastic Processes and their Applications |

巻 | 121 |

発行部数 | 10 |

DOI | |

出版物ステータス | Published - 2011 10 1 |

### フィンガープリント

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics

### これを引用

*Stochastic Processes and their Applications*,

*121*(10), 2416-2454. https://doi.org/10.1016/j.spa.2010.12.005