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Modelling and Forecasting Noisy Realized Volatility

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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”. As 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 2R recently proposed in the literature should be fully correcte d for evaluating forecasts. This paper proposes a full correction of 2 R . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper.

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  • Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Modelling and Forecasting Noisy Realized Volatility," Documentos de Trabajo del ICAE 2011-09, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1109
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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    10. 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.
    11. 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.
    12. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.
    13. 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.
    14. 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.
    15. 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.
    16. Maki, Daiki & Ota, Yasushi, 2021. "Impacts of asymmetry on forecasting realized volatility in Japanese stock markets," Economic Modelling, Elsevier, vol. 101(C).
    17. 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.
    18. 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.
    19. Daiki Maki & Yasushi Ota, 2020. "The impacts of asymmetry on modeling and forecasting realized volatility in Japanese stock markets," Papers 2006.00158, arXiv.org.
    20. 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.
    21. 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).

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    More about this item

    Keywords

    realized volatility; diffusion; financial econometrics; measurement errors; forecasting; model evaluation; goodness-of-fit.;
    All these keywords.

    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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