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A Realized Stochastic Volatility Model With Box-Cox Transformation

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  • Tingguo Zheng
  • Tao Song

Abstract

This article presents a new class of realized stochastic volatility model based on realized volatilities and returns jointly. We generalize the traditionally used logarithm transformation of realized volatility to the Box-Cox transformation, a more flexible parametric family of transformations. A two-step maximum likelihood estimation procedure is introduced to estimate this model on the basis of Koopman and Scharth (2013). Simulation results show that the two-step estimator performs well, and the misspecified log transformation may lead to inaccurate parameter estimation and certain excessive skewness and kurtosis. Finally, an empirical investigation on realized volatility measures and daily returns is carried out for several stock indices.

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  • Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:4:p:593-605
    DOI: 10.1080/07350015.2014.918544
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    Cited by:

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    2. Yuta Kurose & Yasuhiro Omori, "undated". "Multiple-lock Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1075, CIRJE, Faculty of Economics, University of Tokyo.
    3. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    4. Kurose, Yuta & Omori, Yasuhiro, 2020. "Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity," Econometrics and Statistics, Elsevier, vol. 13(C), pages 46-68.
    5. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    6. Li, Shaoyu & Zheng, Tingguo, 2017. "Modeling spot rate using a realized stochastic volatility model with level effect and dynamic drift☆," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 200-221.
    7. Yuta yamauchi & Yasuhiro Omori, 2019. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," CIRJE F-Series CIRJE-F-1117, CIRJE, Faculty of Economics, University of Tokyo.
    8. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1022, CIRJE, Faculty of Economics, University of Tokyo.
    9. Yuta Yamauchi & Yasuhiro Omori, 2018. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," Papers 1809.09928, arXiv.org, revised Mar 2019.
    10. Yuta Yamauchi & Yasuhiro Omori, 2016. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations ," CIRJE F-Series CIRJE-F-1029, CIRJE, Faculty of Economics, University of Tokyo.
    11. Tingguo Zheng & Han Xiao & Rong Chen, 2021. "Generalized Autoregressive Moving Average Models with GARCH Errors," Papers 2105.05532, arXiv.org.
    12. Tingguo Zheng & Han Xiao & Rong Chen, 2022. "Generalized autoregressive moving average models with GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 125-146, January.
    13. Georgios Tsiotas, 2020. "On the use of power transformations in CAViaR models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 296-312, March.

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