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Finite Sample Accuracy Of Integrated Volatility Estimators

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  • Morten Ø. Nielsen

    (Queen's University and CREATES)

  • Per Houmann Frederiksen

    (Nordea Markets)

Abstract

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, the Fourier estimator, and the wavelet estimator, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. Ornstein-Uhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using a model with bid-ask bounce in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bid-ask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias.

Suggested Citation

  • Morten Ø. Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Accuracy Of Integrated Volatility Estimators," Working Paper 1225, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1225
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    Cited by:

    1. Neil Shephard & Ole E. Barndorff-Nielsen & Department of Mathematical Sciences & University of Aarhus & Denmark, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Series Working Papers 240, University of Oxford, Department of Economics.
    2. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    4. Jozef Barunik & Lukas Vacha, 2015. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1347-1364, August.
    5. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
    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. Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    8. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    9. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    10. Wang, Fangfang, 2014. "Optimal design of Fourier estimator in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 708-722.
    11. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2010. "Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 233-261.
    12. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    13. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    14. Recchioni, Maria Cristina & Tedeschi, Gabriele & Gallegati, Mauro, 2015. "A calibration procedure for analyzing stock price dynamics in an agent-based framework," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 1-25.
    15. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    16. S. Sanfelici & S. Ogawa, 2008. "An improved two-step regularization scheme for spot volatility estimation," Economics Department Working Papers 2008-ME02, Department of Economics, Parma University (Italy).
    17. A. Khalifa & S. Hammoudeh & E. Otranto & S. Ramchander, 2012. "Volatility Transmission across Currency, Commodity and Equity Markets under Multi-Chain Regime Switching: Implications for Hedging and Portfolio Allocation," Working Paper CRENoS 201214, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    18. Alva, Kenedy & Romo, Juan & Ruiz Ortega, Esther, 2009. "Modelling intra-daily volatility by functional data analysis: an empirical application to the spanish stock market," DES - Working Papers. Statistics and Econometrics. WS ws092809, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Bent Jesper Christensen & Morten Ø. Nielsen, 2005. "The Implied-realized Volatility Relation With Jumps In Underlying Asset Prices," Working Paper 1186, Economics Department, Queen's University.
    20. Francis In & Sangbae Kim & Vijaya Marisetty & Robert Faff, 2008. "Analysing the performance of managed funds using the wavelet multiscaling method," Review of Quantitative Finance and Accounting, Springer, vol. 31(1), pages 55-70, July.
    21. Maria Cristina Recchioni & Gabriele Tedeschi, 2016. "From bond yield to macroeconomic instability: The effect of negative interest rates," Working Papers 2016/06, Economics Department, Universitat Jaume I, Castellón (Spain).
    22. Ahmed A. A. Khalifa & Hong Miao & Sanjay Ramchander, 2011. "Return distributions and volatility forecasting in metal futures markets: Evidence from gold, silver, and copper," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(1), pages 55-80, January.

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    More about this item

    Keywords

    Bid-ask bounce; finite sample bias; integrated volatility; long memory; market microstructure; Monte Carlo simulation; realized volatility; wavelet;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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