IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i9p2163-2174.html
   My bibliography  Save this article

Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory

Author

Listed:
  • Wei, Yu
  • Chen, Wang
  • Lin, Yu

Abstract

Recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets, but also in emerging markets. Taking high-frequency intraday quotes of the Shanghai Stock Exchange Component (SSEC) Index as example, this paper proposes a new method to measure daily Value-at-Risk (VaR) by combining the newly introduced multifractal volatility (MFV) model and the extreme value theory (EVT) method. Two VaR backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) models. The empirical results show the multifractal nature of price volatility in Chinese stock market. VaR measures based on the multifractal volatility model and EVT method outperform many GARCH-type models at high-risk levels.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:2163-2174
    DOI: 10.1016/j.physa.2013.01.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113000678
    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.2013.01.032?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. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. 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.
    3. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.
    4. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    5. Harvey, Campbell R, 1995. "Predictable Risk and Returns in Emerging Markets," The Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 773-816.
    6. 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.
    7. Gencay, Ramazan & Selcuk, Faruk, 2004. "Extreme value theory and Value-at-Risk: Relative performance in emerging markets," International Journal of Forecasting, Elsevier, vol. 20(2), pages 287-303.
    8. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    9. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    10. Yuan, Ying & Zhuang, Xin-tian, 2008. "Multifractal description of stock price index fluctuation using a quadratic function fitting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 511-518.
    11. 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.
    12. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    13. 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.
    14. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    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. 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.
    17. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    18. 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.
    19. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N., 2001. "Levels of complexity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 16-27.
    20. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    21. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    22. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 49-83.
    23. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    24. Moyano, L.G. & de Souza, J. & Duarte Queirós, S.M., 2006. "Multi-fractal structure of traded volume in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 118-121.
    25. 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.
    26. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    27. 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.
    28. Calvet, Laurent E. & Fisher, Adlai J. & Thompson, Samuel B., 2006. "Volatility comovement: a multifrequency approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 179-215.
    29. 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.
    30. Tabak, Benjamin M. & Cajueiro, Daniel O., 2007. "Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility," Energy Economics, Elsevier, vol. 29(1), pages 28-36, January.
    31. Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing & Chen, Gang, 2011. "Multifractal Fourier detrended cross-correlation analysis of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3670-3678.
    32. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    33. Pont, Oriol & Turiel, Antonio & Pérez-Vicente, Conrad J., 2009. "Empirical evidences of a common multifractal signature in economic, biological and physical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2025-2035.
    34. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
    35. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    36. 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.
    37. Kaushik Matia & Yosef Ashkenazy & H. Eugene Stanley, 2003. "Multifractal Properties of Price Fluctuations of Stocks and Commodities," Papers cond-mat/0308012, arXiv.org.
    38. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    39. Wei, Yu & Huang, Dengshi, 2005. "Multifractal analysis of SSEC in Chinese stock market: A different empirical result from Heng Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 497-508.
    40. He, Ling-Yun & Chen, Shu-Peng, 2011. "Multifractal Detrended Cross-Correlation Analysis of agricultural futures markets," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 355-361.
    41. Zebende, G.F. & da Silva, P.A. & Machado Filho, A., 2011. "Study of cross-correlation in a self-affine time series of taxi accidents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1677-1683.
    42. 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.
    43. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    44. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    45. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    46. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    47. Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    48. J-F. Muzy & D. Sornette & J. delour & A. Arneodo, 2001. "Multifractal returns and hierarchical portfolio theory," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 131-148.
    49. J.-P. Bouchaud & M. Potters & M. Meyer, 2000. "Apparent multifractality in financial time series," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 595-599, February.
    50. He, Ling-Yun & Chen, Shu-Peng, 2011. "Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 297-308.
    51. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    52. Claessens, Stijn & Dasgupta, Susmita & Glen, Jack, 1995. "Return Behavior in Emerging Stock Markets," The World Bank Economic Review, World Bank, vol. 9(1), pages 131-151, January.
    53. Pasquini, Michele & Serva, Maurizio, 1999. "Multiscale behaviour of volatility autocorrelations in a financial market," Economics Letters, Elsevier, vol. 65(3), pages 275-279, December.
    54. Zhuang, Xin-tian & Huang, Xiao-yuan & Sha, Yan-li, 2004. "Research on the fractal structure in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 293-305.
    55. A. Bershadskii, 1999. "Multifractal critical phenomena in traffic and economic processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(2), pages 361-364, September.
    56. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    57. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    58. Stanley, H.E & Amaral, L.A.N & Canning, D & Gopikrishnan, P & Lee, Y & Liu, Y, 1999. "Econophysics: Can physicists contribute to the science of economics?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 156-169.
    59. Hajian, S. & Movahed, M. Sadegh, 2010. "Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4942-4957.
    60. Li, Zhihui & Lu, Xinsheng, 2012. "Cross-correlations between agricultural commodity futures markets in the US and China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3930-3941.
    61. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2007. "Scale invariant distribution and multifractality of volatility multipliers in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 343-350.
    62. 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.
    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. Xin-Lan Fu & Xing-Lu Gao & Zheng Shan & Zhi-Qiang Jiang & Wei-Xing Zhou, 2018. "Multifractal characteristics and return predictability in the Chinese stock markets," Papers 1806.07604, arXiv.org.
    2. Akash P. POOJARI & Siva Kiran GUPTHA & G Raghavender RAJU, 2022. "Multifractal analysis of equities. Evidence from the emerging and frontier banking sectors," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(3(632), A), pages 61-80, Autumn.
    3. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2017. "Risk quantification in turmoil markets," Risk Management, Palgrave Macmillan, vol. 19(3), pages 202-224, August.
    4. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
    5. 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.
    6. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "Semi-nonparametric VaR forecasts for hedge funds during the recent crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 330-343.
    7. 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.
    8. Viviane Naimy & José-María Montero & Rim El Khoury & Nisrine Maalouf, 2020. "Market Volatility of the Three Most Powerful Military Countries during Their Intervention in the Syrian War," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    9. 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.
    10. Gong, Pu & Weng, Yingliang, 2016. "Value-at-Risk forecasts by a spatiotemporal model in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 173-191.

    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. 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.
    2. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2011. "A copula–multifractal volatility hedging model for CSI 300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4260-4272.
    3. Akash P. POOJARI & Siva Kiran GUPTHA & G Raghavender RAJU, 2022. "Multifractal analysis of equities. Evidence from the emerging and frontier banking sectors," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(3(632), A), pages 61-80, Autumn.
    4. 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.
    5. 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.
    6. Dutta, Srimonti & Ghosh, Dipak & Chatterjee, Sucharita, 2016. "Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 188-201.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Wang, Dong-Hua & Yu, Xiao-Wen & Suo, Yuan-Yuan, 2012. "Statistical properties of the yuan exchange rate index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3503-3512.
    12. Zhou, Weijie & Dang, Yaoguo & Gu, Rongbao, 2013. "Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1429-1438.
    13. Liu, Li & Wang, Yudong, 2014. "Cross-correlations between spot and futures markets of nonferrous metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 20-30.
    14. Wang, Yudong & Wu, Chongfeng & Pan, Zhiyuan, 2011. "Multifractal detrending moving average analysis on the US Dollar exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3512-3523.
    15. 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.
    16. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.
    17. Zhuang, Xiaoyang & Wei, Yu & Ma, Feng, 2015. "Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 101-113.
    18. 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.
    19. 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.
    20. Gao, Xing-Lu & Shao, Ying-Hui & Yang, Yan-Hong & Zhou, Wei-Xing, 2022. "Do the global grain spot markets exhibit multifractal nature?," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

    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:392:y:2013:i:9:p:2163-2174. 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.