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Modelling and Forecasting Noisy Realized Volatility

Author

Listed:
  • Manabu Asai

    (Faculty of Economics, Soka University)

  • Michael McAleer

    (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University)

  • Marcelo C. Medeiros

    (Department of Economics, Pontifical Catholic University of Rio de Janeiro)

Abstract

Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called "realized volatility error". Since such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected R2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R2 . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper.

Suggested Citation

  • Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Modelling and Forecasting Noisy Realized Volatility," KIER Working Papers 758, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:758
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    Cited by:

    1. Kenichiro McAlinn & Asahi Ushio & Teruo Nakatsuma, 2020. "Volatility forecasts using stochastic volatility models with nonlinear leverage effects," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 143-154, March.
    2. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2012. "Asymmetry and Long Memory in Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 495-512, June.
    3. Fengler, M.R. & Mammen, E. & Vogt, M., 2015. "Specification and structural break tests for additive models with applications to realized variance data," Journal of Econometrics, Elsevier, vol. 188(1), pages 196-218.
    4. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    5. Duong, Diep & Swanson, Norman R., 2015. "Empirical evidence on the importance of aggregation, asymmetry, and jumps for volatility prediction," Journal of Econometrics, Elsevier, vol. 187(2), pages 606-621.
    6. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    7. Maki, Daiki & Ota, Yasushi, 2021. "Impacts of asymmetry on forecasting realized volatility in Japanese stock markets," Economic Modelling, Elsevier, vol. 101(C).
    8. Hwang, Eunju & Shin, Dong Wan, 2015. "A CUSUMSQ test for structural breaks in error variance for a long memory heterogeneous autoregressive model," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 167-176.
    9. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
    10. G. Mesters & S. J. Koopman & M. Ooms, 2016. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 659-687, April.
    11. Vortelinos, Dimitrios I., 2015. "Out-of-sample evaluation of macro announcements, linearity, long memory, heterogeneity and jumps in mini-futures markets," Review of Financial Economics, Elsevier, vol. 27(C), pages 58-67.
    12. Lin, Boqiang & Wu, Nan, 2022. "Do heterogeneous oil price shocks really have different effects on earnings management?," International Review of Financial Analysis, Elsevier, vol. 79(C).
    13. Dimitrios I. Vortelinos, 2015. "Out‐of‐sample evaluation of macro announcements, linearity, long memory, heterogeneity and jumps in mini‐futures markets," Review of Financial Economics, John Wiley & Sons, vol. 27(1), pages 58-67, November.
    14. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
    15. Lee, Oesook, 2014. "The functional central limit theorem and structural change test for the HAR(∞) model," Economics Letters, Elsevier, vol. 124(3), pages 370-373.
    16. Bekierman, Jeremias & Manner, Hans, 2018. "Forecasting realized variance measures using time-varying coefficient models," International Journal of Forecasting, Elsevier, vol. 34(2), pages 276-287.
    17. Zhao, Yuan & Gong, Xue & Zhang, Weiguo & Xu, Weijun, 2024. "Forecasting carbon futures returns using feature selection and Markov chain with sample distribution," Energy Economics, Elsevier, vol. 140(C).
    18. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.
    19. Claudiu Vinte & Marcel Ausloos & Titus Felix Furtuna, 2022. "A Volatility Estimator of Stock Market Indices Based on the Intrinsic Entropy Model," Papers 2205.01370, arXiv.org.
    20. Hwang, Eunju & Shin, Dong Wan, 2013. "A CUSUM test for a long memory heterogeneous autoregressive model," Economics Letters, Elsevier, vol. 121(3), pages 379-383.
    21. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    22. Daiki Maki & Yasushi Ota, 2020. "The impacts of asymmetry on modeling and forecasting realized volatility in Japanese stock markets," Papers 2006.00158, arXiv.org.

    More about this item

    Keywords

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    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • 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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