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Empirical likelihood for high frequency data

Author

Listed:
  • Camponovo, Lorenzo
  • Matsushita, Yukitoshi
  • Otsu, Taisuke

Abstract

This paper introduces empirical likelihood methods for interval estimation and hypothesis testing on volatility measures in some high frequency data environments. We propose a modified empirical likelihood statistic that is asymptotically pivotal under infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. The proposed statistic is extended to be robust to the presence of jumps and microstructure noise. We also provide an empirical likelihood-based test to detect the presence of jumps. Furthermore, we study higher-order properties of a general family of nonparametric likelihood statistics and show that a particular statistic admits a Bartlett correction: a higher-order refinement to achieve better coverage or size properties. Simulation and a real data example illustrate the usefulness of our approach.

Suggested Citation

  • Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2019. "Empirical likelihood for high frequency data," LSE Research Online Documents on Economics 100320, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:100320
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    File URL: http://eprints.lse.ac.uk/100320/
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    References listed on IDEAS

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    1. Ana-Maria Dumitru & Giovanni Urga, 2011. "Identifying Jumps in Financial Assets: A Comparison Between Nonparametric Jump Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 242-255, October.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    3. Hounyo, Ulrich & Gonçalves, Sílvia & Meddahi, Nour, 2017. "Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise," Econometric Theory, Cambridge University Press, vol. 33(4), pages 791-838, August.
    4. 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.
    5. Prosper Dovonon & Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2019. "Bootstrapping High-Frequency Jump Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 793-803, April.
    6. 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.
    7. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    8. 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.
    9. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
    10. Dovonon, Prosper & Gonçalves, Sílvia & Meddahi, Nour, 2013. "Bootstrapping realized multivariate volatility measures," Journal of Econometrics, Elsevier, vol. 172(1), pages 49-65.
    11. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    12. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    13. Ole E. Barndorff‐Nielsen & Neil 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, May.
    14. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    15. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    16. Ulrich Hounyo & Bezirgen Veliyev, 2016. "Validity of Edgeworth expansions for realized volatility estimators," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    17. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 339-369.
    18. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    19. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    20. Yingying Li & Zhiyuan Zhang & Xinghua Zheng, 2013. "Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise," Papers 1303.5809, arXiv.org.
    21. Renault, Eric & Sarisoy, Cisil & Werker, Bas J.M., 2017. "Efficient Estimation Of Integrated Volatility And Related Processes," Econometric Theory, Cambridge University Press, vol. 33(2), pages 439-478, April.
    22. Gonçalves, Sílvia & Meddahi, Nour, 2011. "Box-Cox transforms for realized volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 129-144, January.
    23. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(4), pages 677-719, August.
    24. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413.
    25. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    26. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    27. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    28. repec:taf:jnlbes:v:30:y:2012:i:2:p:242-255 is not listed on IDEAS
    29. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    30. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    31. Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
    32. Li, Yingying & Zhang, Zhiyuan & Zheng, Xinghua, 2013. "Volatility inference in the presence of both endogenous time and microstructure noise," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2696-2727.
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    More about this item

    Keywords

    Nonparametric methods; Volatility; Microstructure noise; SNP 615882;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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