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Predictive density estimators for daily volatility based on the use of realized measures

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Author Info

  • Corradi, Valentina
  • Distaso, Walter
  • Swanson, Norman R.

Abstract

The main objective of this paper is to propose a feasible, model free estimator of the predictive density of integrated volatility. In this sense, we extend recent papers by Andersen et al. [Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2003. Modelling and forecasting realized volatility. Econometrica 71, 579-626], and by Andersen et al. [Andersen, T.G., Bollerslev, T., Meddahi, N., 2004. Analytic evaluation of volatility forecasts. International Economic Review 45, 1079-1110; Andersen, T.G., Bollerslev, T., Meddahi, N., 2005. Correcting the errors: Volatility forecast evaluation using high frequency data and realized volatilities. Econometrica 73, 279-296], who address the issue of pointwise prediction of volatility via ARMA models, based on the use of realized volatility. Our approach is to use a realized volatility measure to construct a non-parametric (kernel) estimator of the predictive density of daily volatility. We show that, by choosing an appropriate realized measure, one can achieve consistent estimation, even in the presence of jumps and microstructure noise in prices. More precisely, we establish that four well known realized measures, i.e. realized volatility, bipower variation, and two measures robust to microstructure noise, satisfy the conditions required for the uniform consistency of our estimator. Furthermore, we outline an alternative simulation based approach to predictive density construction. Finally, we carry out a simulation experiment in order to assess the accuracy of our estimators, and provide an empirical illustration that underscores the importance of using microstructure robust measures when using high frequency data.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 150 (2009)
Issue (Month): 2 (June)
Pages: 119-138

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Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:119-138

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

Related research

Keywords: Diffusions Integrated volatility Realized volatility measures Kernels Microstructure noise;

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References

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  1. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
  2. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  3. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
  4. 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.
  5. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  6. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  7. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  8. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  9. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
  10. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Subsampling realised kernels," Journal of Econometrics, Elsevier, vol. 160(1), pages 204-219, January.
  11. Ait-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2005. "Ultra high frequency volatility estimation with dependent microstructure noise," Discussion Paper Series 1: Economic Studies 2005,30, Deutsche Bundesbank, Research Centre.
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  14. MEDDAHI, Nour, 2002. "ARMA Representation of Integrated and Realized Variances," Cahiers de recherche 2002-20, Universite de Montreal, Departement de sciences economiques.
  15. Norman R. Swanson & Valentina Corradi & Walter Distaso, 2011. "Predictive Inference for Integrated Volatility," Departmental Working Papers 201108, Rutgers University, Department of Economics.
  16. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
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  18. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
  19. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  20. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
  21. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  22. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  23. Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Series Working Papers 2004-FE-21, University of Oxford, Department of Economics.
  24. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  25. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
  26. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
  27. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  28. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation," Cowles Foundation Discussion Papers 909R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1990.
  29. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, 01.
  30. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
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Citations

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Cited by:
  1. Norman R. Swanson & Valentina Corradi & Walter Distaso, 2011. "Predictive Inference for Integrated Volatility," Departmental Working Papers 201109, Rutgers University, Department of Economics.
  2. Peter Malec & Melanie Schienle, 2012. "Nonparametric Kernel Density Estimation Near the Boundary," SFB 649 Discussion Papers SFB649DP2012-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Shiyi Chen & Wolfgang K. Härdle & Kiho Jeong, 2010. "Forecasting volatility with support vector machine-based GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(4), pages 406-433.
  4. Diep Duong & Norman R. Swanson, 2011. "Volatility in Discrete and Continuous Time Models: A Survey with New Evidence on Large and Small Jumps," Departmental Working Papers 201117, Rutgers University, Department of Economics.
  5. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Post-Print peer-00834423, HAL.
  6. Anisha Ghosh & Oliver Linton, 2009. "Consistent estimation of the risk-return tradeoff in the presence of measurement error," Economics Working Papers we094928, Universidad Carlos III, Departamento de Economía.
  7. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Post-Print hal-00834423, HAL.
  8. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.

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