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Box-Cox transforms for realized volatility

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  • Gonçalves, Sílvia
  • Meddahi, Nour

Abstract

The log transformation of realized volatility is often preferred to the raw version of realized volatility because of its superior finite sample properties. One of the possible explanations for this finding is the fact the skewness of the log transformed statistic is smaller than that of the raw statistic. Simulation evidence presented here shows that this is the case. It also shows that the log transform does not completely eliminate skewness in finite samples. This suggests that there may exist other nonlinear transformations that are more effective at reducing the finite sample skewness. The main goal of this paper is to study the accuracy of a new class of transformations for realized volatility based on the Box-Cox transformation. This transformation is indexed by a parameter [beta] and contains as special cases the log (when [beta]=0) and the raw (when [beta]=1) versions of realized volatility. Based on the theory of Edgeworth expansions, we study the accuracy of the Box-Cox transforms across different values of [beta]. We derive an optimal value of [beta] that approximately eliminates skewness. We then show that the corresponding Box-Cox transformed statistic outperforms other choices of [beta], including [beta]=0 (the log transformation). We provide extensive Monte Carlo simulation results to compare the finite sample properties of different Box-Cox transforms. Across the models considered in this paper, one of our conclusions is that [beta]=-1 (i.e. relying on the inverse of realized volatility also known as realized precision) is the best choice if we want to control the coverage probability of 95% level confidence intervals for integrated volatility.

Suggested Citation

  • Gonçalves, Sílvia & Meddahi, Nour, 2011. "Box-Cox transforms for realized volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 129-144, January.
    • Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:129-144
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    Cited by:

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    3. Lu, Xinjie & Ma, Feng & Wang, Jiqian & Wang, Jianqiong, 2020. "Examining the predictive information of CBOE OVX on China’s oil futures volatility: Evidence from MS-MIDAS models," Energy, Elsevier, vol. 212(C).
    4. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    5. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    6. Peter Reinhard Hansen & Guillaume Horel, 2009. "Quadratic Variation by Markov Chains," CREATES Research Papers 2009-13, Department of Economics and Business Economics, Aarhus University.
    7. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
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    9. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
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    12. Audrino, Francesco & Sigrist, Fabio & Ballinari, Daniele, 2020. "The impact of sentiment and attention measures on stock market volatility," International Journal of Forecasting, Elsevier, vol. 36(2), pages 334-357.

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