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, Bollerslev, Diebold and Labys (2003), and by Andersen, Bollerslev and Meddahi (2004, 2005), 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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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number
200620.
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006.
"Subsampling realised kernels,"
Economics Papers
2006-W10, Economics Group, Nuffield College, University of Oxford.
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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.
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