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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 from Jacod (2008) 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 estimator by Hayashi and Yoshida (2005) 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.

Suggested Citation

  • Markus Bibinger & Mathias Vetter, 2013. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," SFB 649 Discussion Papers SFB649DP2013-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2013-029
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    References listed on IDEAS

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    1. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
    2. Hayashi, Takaki & Yoshida, Nakahiro, 2011. "Nonsynchronous covariation process and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2416-2454, October.
    3. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    4. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
    5. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    6. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    7. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    8. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    9. Fukasawa, Masaaki & Rosenbaum, Mathieu, 2012. "Central limit theorems for realized volatility under hitting times of an irregular grid," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3901-3920.
    10. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    11. Markus Bibinger, 2011. "Asymptotics of Asynchronicity," SFB 649 Discussion Papers SFB649DP2011-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    More about this item

    Keywords

    asynchronous observations; co-jumps; statistics of semimartingales; quadratic covariation;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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