Nonsynchronous covariation process and limit theorems

Takaki Hayashi, Nakahiro Yoshida

研究成果: Article査読

27 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2416-2454
ページ数39
ジャーナルStochastic Processes and their Applications
121
10
DOI
出版ステータスPublished - 2011 10月

ASJC Scopus subject areas

  • 統計学および確率
  • モデリングとシミュレーション
  • 応用数学

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