IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v160y2011i1p129-144.html
   My bibliography  Save this article

Box-Cox transforms for realized volatility

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00068-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(4), pages 677-719, August.
    3. 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.
    4. 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.
    5. 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.
    6. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, November.
    7. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    8. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    9. 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, February.
    10. Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(5), pages 963-987, October.
    11. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu-Min Yen, 2013. "Testing Jumps via False Discovery Rate Control," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-15, April.
    2. 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.
    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.
    8. repec:dau:papers:123456789/6805 is not listed on IDEAS
    9. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    10. Chen, Wang & Lu, Xinjie & Wang, Jiqian, 2022. "Modeling and managing stock market volatility using MRS-MIDAS model," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 625-635.
    11. Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2019. "Empirical likelihood for high frequency data," LSE Research Online Documents on Economics 100320, London School of Economics and Political Science, LSE Library.
    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.

    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. 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.
    2. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
    3. 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.
    4. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
    5. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    6. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    7. Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CARF F-Series CARF-F-145, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Degiannakis, Stavros & Livada, Alexandra, 2013. "Realized volatility or price range: Evidence from a discrete simulation of the continuous time diffusion process," Economic Modelling, Elsevier, vol. 30(C), pages 212-216.
    9. 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.
    10. Vortelinos, Dimitrios I. & Thomakos, Dimitrios D., 2013. "Nonparametric realized volatility estimation in the international equity markets," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 34-45.
    11. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    12. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 326-360, Summer.
    13. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.
    14. Chorro, Christophe & Ielpo, Florian & Sévi, Benoît, 2020. "The contribution of intraday jumps to forecasting the density of returns," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    15. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2010. "Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 233-261.
    16. Julien Chevallier & Benoît Sévi, 2009. "On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting," Working Papers hal-04140871, HAL.
    17. repec:dau:papers:123456789/4598 is not listed on IDEAS
    18. Mykland, Per A. & Zhang, Lan, 2016. "Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price," Journal of Econometrics, Elsevier, vol. 194(2), pages 242-262.
    19. Ysusi Carla, 2006. "Detecting Jumps in High-Frequency Financial Series Using Multipower Variation," Working Papers 2006-10, Banco de México.
    20. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Documents de travail du Centre d'Economie de la Sorbonne 17006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    21. Hua, Jian & Manzan, Sebastiano, 2013. "Forecasting the return distribution using high-frequency volatility measures," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4381-4403.

    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:eee:econom:v:160:y:2011:i:1:p:129-144. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.