[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/aah/create/2007-02.html
   My bibliography  Save this paper

Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach

Author

Listed:
  • Dennis Kristensen

    (School of Economics and Management, University of Aarhus, Denmark)

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.

Suggested Citation

  • Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2007-02
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/07/rp07_02.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    3. 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.
    4. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    6. 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.
    7. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    8. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    10. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..
    11. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    12. 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.
    13. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March.
    14. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    15. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    16. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    17. 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.
    18. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
    19. Andreou, Elena & Ghysels, Eric, 2002. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation, and Empirical Results," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 363-376, July.
    20. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    21. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility of diffusion processes with high frequency data," Economics Letters, Elsevier, vol. 74(3), pages 371-378, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    3. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
    6. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    7. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    8. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
    9. 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.
    10. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
    11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," Center for Financial Institutions Working Papers 02-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
    12. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March.
    13. repec:pse:psecon:2007-11 is not listed on IDEAS
    14. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    15. Degiannakis, Stavros & Livada, Alexandra, 2013. "Realized volatility or price range: Evidence from a discrete simulation of the continuous time diffusion process," Economic Modelling, Elsevier, vol. 30(C), pages 212-216.
    16. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    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. Creel, Michael & Kristensen, Dennis, 2015. "ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 85-108.
    20. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    21. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.

    More about this item

    Keywords

    Diffusion; in-fill asymptotics; kernel estimation; nonparametric; spot volatility; realised volatility;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2007-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.