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Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps

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  • Markus Bibinger

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  • Mathias Vetter

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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

Suggested Citation

  • 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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    References listed on IDEAS

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