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Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes

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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.

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References

  • Andersen T.G., Bollerslev T., Diebold F.X., Labys P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association, 96(453):42–55

    Article  MATH  MathSciNet  Google Scholar 

  • Dacorogna M.M., Gençay R., Müller U.A., Olsen R.B., Pictet O.V. (2001). An Introduction to High-Frequency Finance. San Diego, Academic Press

    Google Scholar 

  • Dacunha-Castelle D., Florens-Zmirou D. (1986). Estimation of the coefficients of diffusion from discrete observations. Stochastics, 19(4):263–284

    MATH  MathSciNet  Google Scholar 

  • Hayashi T., Kusuoka S. (2004). Nonsynchronous covariation measurement for continuous semimartingales. Graduate School of Mathematical Sciences, University of Tokyo, Preprint 2004-21

    Google Scholar 

  • Hayashi, T., Yoshida, N. (2004). Asymptotic normality of nonsynchronous covariance estimators for diffusion processes. Preprint.

  • Hayashi, T., Yoshida, N. (2005a). Estimating correlations with missing observations in continuous diffusion models. Preprint.

  • Hayashi T., Yoshida N. (2005b). On covariance estimation of non-synchronously observed diffusion processes. Bernoulli, 11(2):359–379

    Article  MATH  MathSciNet  Google Scholar 

  • Hayashi, T., Yoshida, N. (2006). Nonsynchronous covariance estimator and limit theorem. Research Memorandum No. 1020, Institute of Statistical Mathematics.

  • Karatzas I., Shreve S.E. (1991). Brownian Motion and Stochastic Calculus, 2nd edn. New York, Springer

    MATH  Google Scholar 

  • Zhang L., Mykland P.A., Aït-Sahalia Y. (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 100(472): 1394–1411

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Keio University, Graduate School of Business Adminstration, 2-1-1 Hiyoshi-honcho, Yokohama, 223-8523, Japan

    Takaki Hayashi

  2. The University of Tokyo, Graduate School of Mathematical Sciences, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Nakahiro Yoshida

Authors
  1. Takaki Hayashi
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  2. Nakahiro Yoshida
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Correspondence to Takaki Hayashi.

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Hayashi, T., Yoshida, N. Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes. AISM 60, 367–406 (2008). https://doi.org/10.1007/s10463-007-0138-0

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  • DOI: https://doi.org/10.1007/s10463-007-0138-0

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