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Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps

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  • Markus Bibinger
  • Mathias Vetter

Abstract

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod for regularly spaced observations are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable central limit theorem for the Hayashi–Yoshida estimator in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed. Copyright The Institute of Statistical Mathematics, Tokyo 2015

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  • Markus Bibinger & Mathias Vetter, 2015. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 707-743, August.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:4:p:707-743
    DOI: 10.1007/s10463-014-0473-x
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    1. Simon Clinet & Yoann Potiron, 2021. "Estimation for high-frequency data under parametric market microstructure noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 649-669, August.
    2. Aït-Sahalia, Yacine & Xiu, Dacheng, 2019. "A Hausman test for the presence of market microstructure noise in high frequency data," Journal of Econometrics, Elsevier, vol. 211(1), pages 176-205.
    3. Yuta Koike & Zhi Liu, 2019. "Asymptotic properties of the realized skewness and related statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 703-741, August.
    4. Ole Martin & Mathias Vetter, 2019. "Laws of large numbers for Hayashi–Yoshida-type functionals," Finance and Stochastics, Springer, vol. 23(3), pages 451-500, July.
    5. Ole Martin & Mathias Vetter, 2020. "The null hypothesis of (common) jumps in case of irregular and asynchronous observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 711-756, September.

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