IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i3p50-880d909009.html
   My bibliography  Save this article

Modeling Realized Variance with Realized Quarticity

Author

Listed:
  • Hiroyuki Kawakatsu

    (Business School, Dublin City University, Dublin 9, D09 Dublin, Ireland)

Abstract

This paper proposes a model for realized variance that exploits information in realized quarticity. The realized variance and quarticity measures are both highly persistent and highly correlated with each other. The proposed model incorporates information from the observed realized quarticity process via autoregressive conditional variance dynamics. It exploits conditional dependence in higher order (fourth) moments in analogy to the class of GARCH models exploit conditional dependence in second moments.

Suggested Citation

  • Hiroyuki Kawakatsu, 2022. "Modeling Realized Variance with Realized Quarticity," Stats, MDPI, vol. 5(3), pages 1-25, September.
  • Handle: RePEc:gam:jstats:v:5:y:2022:i:3:p:50-880:d:909009
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/5/3/50/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2571-905X/5/3/50/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Bickel & Bo Li & Alexandre Tsybakov & Sara Geer & Bin Yu & Teófilo Valdés & Carlos Rivero & Jianqing Fan & Aad Vaart, 2006. "Regularization in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 271-344, September.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    6. 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.
    7. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    8. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    9. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    10. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    11. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    12. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    13. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    14. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
    15. F. Comte & L. Coutin & E. Renault, 2012. "Affine fractional stochastic volatility models," Annals of Finance, Springer, vol. 8(2), pages 337-378, May.
    16. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    17. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    18. Giuseppe Buccheri & Fulvio Corsi, 2021. "HARK the SHARK: Realized Volatility Modeling with Measurement Errors and Nonlinear Dependencies," Journal of Financial Econometrics, Oxford University Press, vol. 19(4), pages 614-649.
    19. José Da Fonseca & Wenjun Zhang, 2019. "Volatility of volatility is (also) rough," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 600-611, May.
    20. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    21. 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.
    22. 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.
    23. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    24. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, September.
    25. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    26. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    27. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    28. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
    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. Papantonis, Ioannis & Rompolis, Leonidas & Tzavalis, Elias, 2023. "Improving variance forecasts: The role of Realized Variance features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1221-1237.
    2. Papantonis Ioannis & Tzavalis Elias & Agapitos Orestis & Rompolis Leonidas S., 2023. "Augmenting the Realized-GARCH: the role of signed-jumps, attenuation-biases and long-memory effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(2), pages 171-198, April.
    3. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    4. Sharma, Prateek & Vipul,, 2016. "Forecasting stock market volatility using Realized GARCH model: International evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 222-230.
    5. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    6. Tian, Fengping & Yang, Ke & Chen, Langnan, 2017. "Realized volatility forecasting of agricultural commodity futures using the HAR model with time-varying sparsity," International Journal of Forecasting, Elsevier, vol. 33(1), pages 132-152.
    7. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    8. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2014. "Realized volatility models and alternative Value-at-Risk prediction strategies," Economic Modelling, Elsevier, vol. 40(C), pages 101-116.
    9. Barunik, Jozef & Krehlik, Tomas & Vacha, Lukas, 2016. "Modeling and forecasting exchange rate volatility in time-frequency domain," European Journal of Operational Research, Elsevier, vol. 251(1), pages 329-340.
    10. Maheu, John M. & McCurdy, Thomas H., 2011. "Do high-frequency measures of volatility improve forecasts of return distributions?," Journal of Econometrics, Elsevier, vol. 160(1), pages 69-76, January.
    11. Lyócsa, Štefan & Molnár, Peter & Výrost, Tomáš, 2021. "Stock market volatility forecasting: Do we need high-frequency data?," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1092-1110.
    12. Wen Cheong Chin & Min Cherng Lee, 2018. "S&P500 volatility analysis using high-frequency multipower variation volatility proxies," Empirical Economics, Springer, vol. 54(3), pages 1297-1318, May.
    13. Rossi, Eduardo & Santucci de Magistris, Paolo, 2013. "Long memory and tail dependence in trading volume and volatility," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 94-112.
    14. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    15. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    16. Palandri, Alessandro, 2015. "Do negative and positive equity returns share the same volatility dynamics?," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 486-505.
    17. Elena Ivona Dumitrescu & Georgiana-Denisa Banulescu, 2019. "Do High-frequency-based Measures Improve Conditional Covariance Forecasts?," Post-Print hal-03331122, HAL.
    18. Andersen, Torben G. & Bollerslev, Tim & Huang, Xin, 2011. "A reduced form framework for modeling volatility of speculative prices based on realized variation measures," Journal of Econometrics, Elsevier, vol. 160(1), pages 176-189, January.
    19. Yaojie Zhang & Yudong Wang & Feng Ma & Yu Wei, 2022. "To jump or not to jump: momentum of jumps in crude oil price volatility prediction," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-31, December.
    20. Xu, Yongdeng, 2022. "The Exponential HEAVY Model: An Improved Approach to Volatility Modeling and Forecasting," Cardiff Economics Working Papers E2022/5, Cardiff University, Cardiff Business School, Economics Section.

    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:gam:jstats:v:5:y:2022:i:3:p:50-880:d:909009. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.