Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes

Takaki Hayashi, Nakahiro Yoshida

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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
Volume60
Issue number2
DOIs
Publication statusPublished - 2008 Jun

Fingerprint

Asymptotic Normality
Diffusion Process
Estimator
Bernoulli
Synchronization
Interval
Zero
Observation

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes. / Hayashi, Takaki; Yoshida, Nakahiro.

In: Annals of the Institute of Statistical Mathematics, Vol. 60, No. 2, 06.2008, p. 367-406.

Research output: Contribution to journalArticle

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