IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v427y2015icp50-61.html
   My bibliography  Save this article

High and low or close to close prices? Evidence from the multifractal volatility

Author

Listed:
  • Liu, Zhichao
  • Ma, Feng
  • Long, Yujia

Abstract

In this study, we examine the daily returns and daily range returns dependent on close–close and the high–low prices when forecasting multifractal volatility in the Chinese stock market. In in-sample forecasting we find that both the daily returns and range returns have a significant impact on the future multifractal volatility, existing the well-established phenomenon of “leverage effects” of the positive and negative returns. Moreover, using the MF-DFA method, we find that both the two series present the persistence and exhibit the multifractal features. Furthermore, our MCS test results show that the ARFIMA-lnMFV-R and ARFIMA-lnMFV-LR models provide relatively superior volatility forecasts in comparison to all other models. Finally, we find that the daily returns calculated by close to close prices have a greater power than the daily range return calculated by high and low prices in forecasting.

Suggested Citation

  • Liu, Zhichao & Ma, Feng & Long, Yujia, 2015. "High and low or close to close prices? Evidence from the multifractal volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 50-61.
  • Handle: RePEc:eee:phsmap:v:427:y:2015:i:c:p:50-61
    DOI: 10.1016/j.physa.2015.02.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115001600
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2015.02.054?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    2. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    3. Figlewski, Stephen, 1981. "Futures Trading and Volatility in the GNMA Market," Journal of Finance, American Finance Association, vol. 36(2), pages 445-456, May.
    4. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    5. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    6. Haugom, Erik & Langeland, Henrik & Molnár, Peter & Westgaard, Sjur, 2014. "Forecasting volatility of the U.S. oil market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 1-14.
    7. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    8. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    9. Bollerslev, Tim & Melvin, Michael, 1994. "Bid--ask spreads and volatility in the foreign exchange market : An empirical analysis," Journal of International Economics, Elsevier, vol. 36(3-4), pages 355-372, May.
    10. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    11. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2010. "Cross-correlations between Chinese A-share and B-share markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5468-5478.
    12. George H. K. Wang & Jot Yau, 2000. "Trading volume, bid–ask spread, and price volatility in futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(10), pages 943-970, November.
    13. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    14. Sun, Xia & Chen, Huiping & Wu, Ziqin & Yuan, Yongzhuang, 2001. "Multifractal analysis of Hang Seng index in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 553-562.
    15. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    16. Neda Todorova & Sven Husmann, 2012. "A comparative study of range‐based stock return volatility estimators for the German market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(6), pages 560-586, June.
    17. Wei, Yu & Wang, Peng, 2008. "Forecasting volatility of SSEC in Chinese stock market using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1585-1592.
    18. Lopez, Jose A, 2001. "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 87-109, March.
    19. Agnolucci, Paolo, 2009. "Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models," Energy Economics, Elsevier, vol. 31(2), pages 316-321, March.
    20. 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.
    21. Wang, Yudong & Liu, Li & Gu, Rongbao, 2009. "Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 271-276, December.
    22. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    23. James Doran & Ehud Ronn, 2005. "The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets," Review of Derivatives Research, Springer, vol. 8(3), pages 177-198, December.
    24. Chaiyuth Padungsaksawasdi & Robert T. Daigler, 2014. "The Return‐Implied Volatility Relation for Commodity ETFs," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(3), pages 261-281, March.
    25. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    26. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
    27. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    28. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
    29. Ma, Feng & Wei, Yu & Huang, Dengshi, 2013. "Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1659-1670.
    30. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    31. Wei, Yu & Chen, Wang & Lin, Yu, 2013. "Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2163-2174.
    32. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
    33. Paul Berhanu Girma & Mbodja Mougoué, 2002. "An empirical examination of the relation between futures spreads volatility, volume, and open interest," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(11), pages 1083-1102, November.
    34. Chen, Hongtao & Wu, Chongfeng, 2011. "Forecasting volatility in Shanghai and Shenzhen markets based on multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(16), pages 2926-2935.
    35. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    36. Sun, Xia & Chen, Huiping & Yuan, Yongzhuang & Wu, Ziqin, 2001. "Predictability of multifractal analysis of Hang Seng stock index in Hong Kong," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 473-482.
    37. Yan-Leung Cheung & Yin-Wong Cheung & Alan T. K. Wan, 2009. "A high-low model of daily stock price ranges," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 103-119.
    38. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    39. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    40. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    41. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    42. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    43. Ma, Feng & Wei, Yu & Huang, Dengshi & Chen, Yixiang, 2014. "Which is the better forecasting model? A comparison between HAR-RV and multifractality volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 171-180.
    44. Neda Todorova, 2012. "Volatility estimators based on daily price ranges versus the realized range," Applied Financial Economics, Taylor & Francis Journals, vol. 22(3), pages 215-229, February.
    45. Liu, Li & Wan, Jieqiu, 2012. "A study of Shanghai fuel oil futures price volatility based on high frequency data: Long-range dependence, modeling and forecasting," Economic Modelling, Elsevier, vol. 29(6), pages 2245-2253.
    46. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.
    47. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    2. Gong, Xu & Lin, Boqiang, 2018. "Structural changes and out-of-sample prediction of realized range-based variance in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 27-39.
    3. Xie, Nan & Wang, Zongrun & Chen, Sicen & Gong, Xu, 2019. "Forecasting downside risk in China’s stock market based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 530-541.
    4. Peng, Huan & Chen, Ruoxun & Mei, Dexiang & Diao, Xiaohua, 2018. "Forecasting the realized volatility of the Chinese stock market: Do the G7 stock markets help?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 78-85.

    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. Ma, Feng & Wei, Yu & Huang, Dengshi & Chen, Yixiang, 2014. "Which is the better forecasting model? A comparison between HAR-RV and multifractality volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 171-180.
    2. Tao, Qizhi & Wei, Yu & Liu, Jiapeng & Zhang, Ting, 2018. "Modeling and forecasting multifractal volatility established upon the heterogeneous market hypothesis," International Review of Economics & Finance, Elsevier, vol. 54(C), pages 143-153.
    3. Liu, Zhicao & Ye, Yong & Ma, Feng & Liu, Jing, 2017. "Can economic policy uncertainty help to forecast the volatility: A multifractal perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 181-188.
    4. Wei, Yu & Chen, Wang & Lin, Yu, 2013. "Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2163-2174.
    5. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    6. Feng Ma & Yu Wei & Wang Chen & Feng He, 2018. "Forecasting the volatility of crude oil futures using high-frequency data: further evidence," Empirical Economics, Springer, vol. 55(2), pages 653-678, September.
    7. Yuan, Ying & Zhang, Tonghui, 2020. "Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Wang Pu & Yixiang Chen & Feng Ma, 2016. "Forecasting the realized volatility in the Chinese stock market: further evidence," Applied Economics, Taylor & Francis Journals, vol. 48(33), pages 3116-3130, July.
    9. Ma, Feng & Li, Yu & Liu, Li & Zhang, Yaojie, 2018. "Are low-frequency data really uninformative? A forecasting combination perspective," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 92-108.
    10. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    11. Chen, Hongtao & Wu, Chongfeng, 2011. "Forecasting volatility in Shanghai and Shenzhen markets based on multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(16), pages 2926-2935.
    12. Ruan, Qingsong & Zhang, Manqian & Lv, Dayong & Yang, Haiquan, 2018. "SAD and stock returns revisited: Nonlinear analysis based on MF-DCCA and Granger test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1009-1022.
    13. Haugom, Erik & Langeland, Henrik & Molnár, Peter & Westgaard, Sjur, 2014. "Forecasting volatility of the U.S. oil market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 1-14.
    14. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
    15. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    16. Di Sanzo, Silvestro, 2018. "A Markov switching long memory model of crude oil price return volatility," Energy Economics, Elsevier, vol. 74(C), pages 351-359.
    17. Wang, Yudong & Wu, Chongfeng, 2012. "Forecasting energy market volatility using GARCH models: Can multivariate models beat univariate models?," Energy Economics, Elsevier, vol. 34(6), pages 2167-2181.
    18. Duan, Yinying & Chen, Wang & Zeng, Qing & Liu, Zhicao, 2018. "Leverage effect, economic policy uncertainty and realized volatility with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 148-154.
    19. Cao, Guangxi & Cao, Jie & Xu, Longbing, 2013. "Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 797-807.
    20. Mei, Dexiang & Liu, Jing & Ma, Feng & Chen, Wang, 2017. "Forecasting stock market volatility: Do realized skewness and kurtosis help?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 153-159.

    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:phsmap:v:427:y:2015:i:c:p:50-61. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.