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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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    References listed on IDEAS

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    8. Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(05), pages 963-987, October.
    9. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    10. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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    Citations

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    Cited by:

    1. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    2. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    3. 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.
    4. Nick Taylor, 2016. "Realised Variance Forecasting Under Box-Cox Transformations," Bristol Accounting and Finance Discussion Papers 16/4, School of Economics, Finance, and Management, University of Bristol, UK.
    5. Peter Reinhard Hansen & Guillaume Horel, 2009. "Quadratic Variation by Markov Chains," CREATES Research Papers 2009-13, Department of Economics and Business Economics, Aarhus University.
    6. Daniel PREVE & Anders ERIKSSON & Jun YU, 2009. "Forecasting Realized Volatility Using A Nonnegative Semiparametric Model," Working Papers 22-2009, Singapore Management University, School of Economics.
    7. repec:dau:papers:123456789/6805 is not listed on IDEAS
    8. repec:eee:intfor:v:33:y:2017:i:4:p:770-785 is not listed on IDEAS

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