Box-Cox transforms for realized volatility
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.
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- Phillips, Peter C B & Park, Joon Y, 1988.
"On the Formulation of Wald Tests of Nonlinear Restrictions,"
Econometric Society, vol. 56(5), pages 1065-83, September.
- Peter C.B. Phillips & Joon Y. Park, 1986. "On the Formulation of Wald Tests of Nonlinear Restrictions," Cowles Foundation Discussion Papers 801, Cowles Foundation for Research in Economics, Yale University.
- Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006.
"Limit Theorems For Bipower Variation In Financial Econometrics,"
Cambridge University Press, vol. 22(04), pages 677-719, August.
- Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers 2005-FE-09, University of Oxford, Department of Economics.
- Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," OFRC Working Papers Series 2005fe09, Oxford Financial Research Centre.
- 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.
- Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
- Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(05), pages 963-987, October.
- Ole E. Barndorff-Nielsen, 2004.
"Power and Bipower Variation with Stochastic Volatility and Jumps,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(1), pages 1-37.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
- Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2000.
"Econometric analysis of realised volatility and its use in estimating stochastic volatility models,"
2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
- Ole E. Barndorff-Nielsen & 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.
- Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
- Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
- Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130.
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