Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes

Takaki Hayashi, Nakahiro Yoshida

Research output: Contribution to journalArticle

35 Citations (Scopus)


We consider the problem of estimating the covariance of two diffusion-type processes when they are observed only at discrete times in a nonsynchronous manner. In our previous work in 2003, we proposed a new estimator which is free of any 'synchronization' processing of the original data and showed that it is consistent for the true covariance of the processes as the observation interval shrinks to zero; Hayashi and Yoshida (Bernoulli, 11, 359-379, 2005). This paper is its sequel. Specifically, it establishes asymptotic normality of the estimator in a general nonsynchronous sampling scheme.

Original languageEnglish
Pages (from-to)367-406
Number of pages40
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
Publication statusPublished - 2008 Jun 1



  • Diffusions
  • Discrete-time observations
  • High-frequency data
  • Nonsynchronicity
  • Quadratic variation
  • Realized volatility

ASJC Scopus subject areas

  • Statistics and Probability

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