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Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach

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  • Kristensen, Dennis

Abstract

A kernel weighted version of the standard realised integrated volatility es- timator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realised spot volatility is obtained. We denote this the filtered spot volatility. We show con- sistency and asymptotic normality of the kernel smoothed realised volatility and the filtered spot volatility. The choice of bandwidth is discussed and data- driven selection methods proposed. A simulation study examines the finite sample properties of the estimators.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 01 (February)
Pages: 60-93

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Handle: RePEc:cup:etheor:v:26:y:2010:i:01:p:60-93_09

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  1. D. Blanke, 2002. "Estimation of Local Smoothness Coefficients for Continuous Time Processes," Statistical Inference for Stochastic Processes, Springer, vol. 5(1), pages 65-93, January.
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Cited by:
  1. Andrew Ang & Dennis Kristensen, 2011. "Testing Conditional Factor Models," NBER Working Papers 17561, National Bureau of Economic Research, Inc.
  2. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, School of Economics and Management, University of Aarhus.
  3. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
  4. Fulvio Corsi & Davide Pirino & Roberto Renò, 2008. "Volatility forecasting: the jumps do matter," Department of Economics University of Siena 534, Department of Economics, University of Siena.
  5. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," Working Papers - Mathematical Economics 2012-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  6. Sujin Park & Oliver Linton, 2012. "Estimating the Quadratic Covariation Matrix for an Asynchronously Observed Continuous Time Signal Masked by Additive Noise," FMG Discussion Papers dp703, Financial Markets Group.
  7. Almut E. D. Veraart, 2010. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," CREATES Research Papers 2010-65, School of Economics and Management, University of Aarhus.
  8. Morten L. Bech & Yvan Lengwiler, 2012. "The Financial Crisis and the Changing Dynamics of the Yield Curve," Working papers 2012/06, Faculty of Business and Economics - University of Basel.
  9. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers 2008-37, School of Economics and Management, University of Aarhus.
  10. Selma Chaker, 2013. "Volatility and Liquidity Costs," Working Papers 13-29, Bank of Canada.
  11. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
  12. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
  13. Kris Boudt & Sébastien Laurent & Asger Lunde & Rogier Quaedvlieg, 2014. "Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity," CREATES Research Papers 2014-05, School of Economics and Management, University of Aarhus.
  14. Boudt, Kris & Cornelissen, Jonathan & Croux, Christophe, 2012. "Jump robust daily covariance estimation by disentangling variance and correlation components," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 2993-3005.
  15. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.

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