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Quasi-maximum likelihood estimation of volatility with high frequency data

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  • Xiu, Dacheng

Abstract

This paper investigates the properties of the well-known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise, by extending the classic asymptotic results of quasi-maximum likelihood estimation. When trying to estimate the integrated volatility and the variance of noise, this parametric approach remains consistent, efficient and robust as a quasi-estimator under misspecified assumptions. Moreover, it shares the model-free feature with nonparametric alternatives, for instance realized kernels, while being advantageous over them in terms of finite sample performance. In light of quadratic representation, this estimator behaves like an iterative exponential realized kernel asymptotically. Comparisons with a variety of implementations of the Tukey-Hanning2 kernel are provided using Monte Carlo simulations, and an empirical study with the Euro/US Dollar future illustrates its application in practice.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 159 (2010)
Issue (Month): 1 (November)
Pages: 235-250

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Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:235-250

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Integrated volatility Market microstructure noise Quasi-maximum likelihood estimator Realized kernels Stochastic volatility;

References

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Citations

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Cited by:
  1. Aït-Sahalia, Yacine & Jacod, Jean & Li, Jia, 2012. "Testing for jumps in noisy high frequency data," Journal of Econometrics, Elsevier, vol. 168(2), pages 207-222.
  2. Norman R. Swanson & Valentina Corradi & Walter Distaso, 2011. "Predictive Inference for Integrated Volatility," Departmental Working Papers 201109, Rutgers University, Department of Economics.
  3. Markus Bibinger & Per A. Mykland, 2013. "Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing," SFB 649 Discussion Papers SFB649DP2013-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Ulrich Hounyo & Sílvia Goncalves & Nour Meddahi, 2013. "Bootstrapping pre-averaged realized volatility under market microstructure noise," CREATES Research Papers 2013-28, School of Economics and Management, University of Aarhus.
  5. 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.
  6. Corsi, Fulvio & Peluso, Stefano & Audrino, Francesco, 2012. "Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation," Economics Working Paper Series 1202, University of St. Gallen, School of Economics and Political Science.
  7. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.
  8. Randolf Altmeyer & Markus Bibinger, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers SFB649DP2014-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Markus Bibinger & Lars Winkelmann, 2013. "Econometrics of co-jumps in high-frequency data with noise," SFB 649 Discussion Papers SFB649DP2013-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Bibinger, Markus, 2012. "An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2411-2453.
  11. Liu, Cheng & Tang, Cheng Yong, 2014. "A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data," Journal of Econometrics, Elsevier, vol. 180(2), pages 217-232.
  12. Markus Bibinger & Markus Reiß, 2011. "Spectral estimation of covolatility from noisy observations using local weights," SFB 649 Discussion Papers SFB649DP2011-086, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  13. Yacine A�t-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-50, December.
  14. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.

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