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Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales

Author

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  • Veraart, Almut E.D.

Abstract

Recent research has focused on modeling asset prices by Itô semimartingales. In such a modeling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realized variance and realized multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realized variance and realized multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory that is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory.

Suggested Citation

  • Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(2), pages 331-368, April.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:331-368_10
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    Cited by:

    1. Yu-Min Yen, 2013. "Testing Jumps via False Discovery Rate Control," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-15, April.
    2. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    3. 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.
    4. Liu, Qiang & Liu, Yiqi & Liu, Zhi & Wang, Li, 2018. "Estimation of spot volatility with superposed noisy data," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 62-79.
    5. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 253-291, September.
    6. Cecilia Mancini & Vanessa Mattiussi & Roberto Renò, 2015. "Spot volatility estimation using delta sequences," Finance and Stochastics, Springer, vol. 19(2), pages 261-293, April.
    7. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, Department of Economics and Business Economics, Aarhus University.
    8. José E. Figueroa-López & Jeffrey Nisen, 2019. "Second-order properties of thresholded realized power variations of FJA additive processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 431-474, October.
    9. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2011. "Ambit Processes and Stochastic Partial Differential Equations," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 35-74, Springer.
    10. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    11. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    12. Lena Cleanthous & Pany Karamanou, 2011. "The ECB Monetary Policy and the Current Financial Crisis," Working Papers 2011-1, Central Bank of Cyprus.
    13. Per A. Mykland & Neil Shephard & Kevin Sheppard, 2012. "Efficient and feasible inference for the components of financial variation using blocked multipower variation," Economics Papers 2012-W02, Economics Group, Nuffield College, University of Oxford.
    14. Dungey, Mardi & Henry, Olan T & Hvodzdyk, Lyudmyla, 2013. "The impact of jumps and thin trading on realized hedge ratios," Working Papers 2013-02, University of Tasmania, Tasmanian School of Business and Economics, revised 28 Mar 2013.
    15. Mathias Vetter, 2021. "A universal approach to estimate the conditional variance in semimartingale limit theorems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1089-1125, December.
    16. Alexander Alvarez & Fabien Panloup & Monique Pontier & Nicolas Savy, 2012. "Estimation of the instantaneous volatility," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 27-59, April.
    17. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, Department of Economics and Business Economics, Aarhus University.
    18. Dungey, Mardi & Hvozdyk, Lyudmyla, 2010. "Cojumping: Evidence from the US Treasury Bond and Future Markets (Discussion Paper 2010-06)," Working Papers 10450, University of Tasmania, Tasmanian School of Business and Economics, revised 14 Jul 2010.
    19. repec:hum:wpaper:sfb649dp2013-029 is not listed on IDEAS
    20. Dungey, Mardi & Hvozdyk, Lyudmyla, 2012. "Cojumping: Evidence from the US Treasury bond and futures markets," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1563-1575.
    21. repec:dau:papers:123456789/6805 is not listed on IDEAS
    22. Bibinger, Markus & Vetter, Mathias, 2013. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," SFB 649 Discussion Papers 2013-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2009. "Stochastic volatility of volatility in continuous time," CREATES Research Papers 2009-25, Department of Economics and Business Economics, Aarhus University.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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