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Asymmetric Multifractal Detrended Fluctuation Analysis (A-MFDFA)

  • Guangxi CaoEmail author
  • Ling-Yun He
  • Jie Cao
Chapter

Abstract

The presence of multifractality suggests the inefficiency (Cajueiro and Tabak 2004, 2004, 2008; Cajueiro et al. 2009; Tabak and Cajueiro 2007; Wang et al. 2010), volatility predictability (Wei and Wang 2008), crash predictions (Wei and Wang 2008; Grech and Pamula 2008), and complexity (Matia et al. 2003; Kumar and Deo 2009; Norouzzadeh and Jafari 2005) of the market.

References

  1. S. Abosedra, H. Baghestani. On the predictive accuracy of crude oil futures prices. Energ. Policy. 32(12), 1389–1393 (2004)Google Scholar
  2. J. Alvarez-Ramirez, E. Rodriguez, J.C. Echeverria, A DFA approach for assessing asymmetric correlations. Phys. A 388, 2263–2270 (2009)CrossRefGoogle Scholar
  3. A. Ang, G. Bekaert, International asset allocation with regime shifts. ‎Rev. Financial Stud. 15(4), 1137–1187 (2002)Google Scholar
  4. A. Ang, J. Chen, Asymmetric correlations of equity portfolios. J. Financ. Econ. 63, 443–494 (2002)Google Scholar
  5. K.H. Bae, G.A. Karolyi, R.M. Stulz, A new approach to measuring financial market contagion. Rev. Financial Stud. 16, 717–764 (2003)Google Scholar
  6. M.Y. Bai, H.B. Zhu, Power law and multiscaling properties of the Chinese stock market. Phys. A 389, 1883–1890 (2010)CrossRefGoogle Scholar
  7. J. Barunik, T. Aste, T.D. Matteo, R.-P. Liu, Understanding the source of multifractality in financial markets. Phys. A 391, 4234–4251 (2012)CrossRefGoogle Scholar
  8. A. Bera, C. Jarque, Efficient tests for normality, heteroskedasticity and serial independence of regression residuals: Monte Carlo evidence. Econ. Lett. 7, 313–318 (1981)CrossRefGoogle Scholar
  9. M.I. Bogachev, J.F. Eichner, A. Bunde, Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets. Phys. Rev. Lett. 99, 240601 (2007)CrossRefGoogle Scholar
  10. D.O. Cajueiro, B.M. Tabak, Ranking efficiency for emerging markets. Chaos Solitons Fractals 22, 349–352 (2004a)CrossRefGoogle Scholar
  11. D.O. Cajueiro, B.M. Tabak, The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient. Phys. A 336, 521–537 (2004b)CrossRefGoogle Scholar
  12. D.O. Cajueiro, B.M. Tabak, Testing for time-varying long-range dependence in real state equity returns. Chaos Solitons Fractals 38, 293–307 (2008)CrossRefGoogle Scholar
  13. D.O. Cajueiro, P. Gogas, B.M. Tabak, Does financial market liberalization increase the degree of market efficiency? The case of the Athens stock exchange. Int. Rev. Financial Anal. 18, 50–57 (2009)CrossRefGoogle Scholar
  14. G.X. Cao, L.B. Xu, J.Cao, Multifractal detrended cross-correlations between the Chinese exchange market and stock market. Phys. A, 4855–4866 (2012)Google Scholar
  15. G. Cao, J. Cao, L. Xu, Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA. Phys. A: Statistical Mechanics and its Applications. 392(4), 797–807 (2013)Google Scholar
  16. C.P. Cristescu, C. Stan, E.I. Scarlat, T. Minea, C.M. Cristescu, Parameter motivated mutual correlation analysis: application to the study of currency exchange rates based on intermittency parameter and Hurst exponent. Phys. A 391, 2623–2635 (2012)Google Scholar
  17. L. Czarnecki, D. Grech, Multifractal dynamics of stock markets. Acta Phys. Pol. A 117, 623–629 (2010)CrossRefGoogle Scholar
  18. R. Demirer, in Asymmetric Correlation of Futures Markets and Optimal Hedging, (2003). http://webradio.siue.edu/business/econfin/pdf/demirer-charnes.pdf
  19. G.X. Du, X.X. Ning, Multifractal properties of Chinese stock market in Shanghai. Phys. A 387, 261–269 (2008)CrossRefGoogle Scholar
  20. M.R. Eldridge, C. Bernbarde, I. Mulvey, Evidence of Chaos in the S&P 500 cash index. Adv. Futures Options Res. 6, 179–192 (1993)Google Scholar
  21. D. Grech, Z. Mazur, Can one make any crash prediction in finance using the local hurst exponent idea? Phys. A 336, 133–145 (2004)CrossRefGoogle Scholar
  22. D. Grech, G. Pamula, The local hurst exponent of the financial time series in the vicinity of crashes on the polish stock exchange market. Phys. A 387, 4299–4308 (2008)CrossRefGoogle Scholar
  23. M.T. Greene, B.D. Fieltz, Long term dependence in common stock returns. J. Financ. Econ. 4, 249–339 (1997)Google Scholar
  24. Z.Q. Jiang, W.X. Zhou, Multifractal analysis of Chinese stock volatilities based on the partition function approach. Phys. A 387, 4881–4888 (2008)CrossRefGoogle Scholar
  25. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316, 87–114 (2002)CrossRefGoogle Scholar
  26. S. Kumar, N. Deo, Multifractal properties of the Indian financial market. Phys. A 388, 1593–1602 (2009)CrossRefGoogle Scholar
  27. G. Lim, S. Kim, H. Lee, K. Kim, D.-I. Lee, Multifractal detrended fluctuation analysis of derivative and spot markets. Phys. A 386, 259–266 (2007)CrossRefGoogle Scholar
  28. F. Longin, B. Solnik, Extreme correlation of international equity markets. J. Finance 56, 649–676 (2001)CrossRefGoogle Scholar
  29. B.B. Mandelbrot, Negative fractal dimensions and multifractals. Phys. A 163, 306–315 (1990)CrossRefGoogle Scholar
  30. B.B. Mandelbrot, Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Proc. R. Soc. Lond. Ser. A 434, 79–88 (1991)CrossRefGoogle Scholar
  31. K. Matia, Y. Ashkenazy, H.E. Stanley, Multifractal properties of price fluctuations of stock and commodities. Europhys. Lett. 61, 422–428 (2003)CrossRefGoogle Scholar
  32. T.D. Matteo, Multi-scaling in finance. Quant. Finance 7, 21–36 (2007)CrossRefGoogle Scholar
  33. P. Norouzzadeh, G.R. Jafari, Application of multifractal measures to Tehran price index. Phys. A 356, 609–627 (2005)CrossRefGoogle Scholar
  34. P. Norouzzadeh, B. Rahmani, A multifractal detrended fluctuation description of Iranian rial-US dollar exchange rate. Phys. A 367, 328–336 (2006)CrossRefGoogle Scholar
  35. C.K. Peng, S.V. Buldyrev, S. Havlin et al., Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689 (1994)CrossRefGoogle Scholar
  36. B. Podobnik, H.E. Stanley, Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. Phys. Rev. Lett. 100, 084102 (2008)CrossRefGoogle Scholar
  37. B. Podobnik, D.F. Fu, H.E. Stanley, PCh. Ivanov, Power-law autocorrelated stochastic processes with long-range cross-correlations. Eur. Phys. J. B 56, 47–52 (2007)CrossRefGoogle Scholar
  38. F. Schmitt, D. Schertzer, S. Lovejoy, Multifractal fluctuations in finance. Int. J. Theor. Appl. Finance 3, 361–364 (2000)CrossRefGoogle Scholar
  39. J. Schmittbuhl, J.-P. Vilotte, S. Roux. Reliability of self-affine measurements. Phys. Rev. E. 51(1), 131 (1995)Google Scholar
  40. H.E. Stanley, V. Plerou, Scaling and universality in economics: empirical results and theoretical interpretation. Quant. Finance 1, 563–567 (2001)CrossRefGoogle Scholar
  41. B.M. Tabak, D.O. Cajueiro, Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility. Energy Econ. 29, 28–36 (2007)CrossRefGoogle Scholar
  42. Y.D. Wang, L. Liu, R.B. Gu, Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis. Int. Rev. Financial Anal. 18, 271–276 (2009)CrossRefGoogle Scholar
  43. Y.D. Wang, L. Liu, R.B. Gu, J.J. Cao, H.Y. Wang, Analysis of market efficiency for the Shanghai stock market over time. Phys. A 389, 1635–1642 (2010)CrossRefGoogle Scholar
  44. Y.D. Wang, C.F. Wu, Z.Y. Pan, Multifractal detrending moving average analysis on the US Dollar exchange rates. Phys. A 390, 3512–3523 (2011a)CrossRefGoogle Scholar
  45. Y.D. Wang, Y. Wei, C.F. Wu, Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil. Phys. A 390, 864–875 (2011b)CrossRefGoogle Scholar
  46. Y. Wei, D.S. Huang, Multifractal analysis of SSEC in Chinese stock market: a different empirical results from Heng Seng index. Phys. A 355, 497–508 (2005)CrossRefGoogle Scholar
  47. Y. Wei, P. Wang, Forecasting volatility of SSEC in Chinese stock market using multifractal analysis. Phys. A 387, 1585–1592 (2008)CrossRefGoogle Scholar
  48. Y. Yuan, X.T. Zhuang, Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis. Phys. A 388, 2189–2197 (2009)CrossRefGoogle Scholar
  49. W.X. Zhou, Multifractal detrended cross-correlation analysis for two nonstationary signals. Phys. Rev. E 77, 066211 (2008)CrossRefGoogle Scholar
  50. W.X. Zhou, The components of empirical multifractality in financial returns. Europhys. Lett. 88, 28004 (2009)CrossRefGoogle Scholar
  51. W.X. Zhou, Finite-size effect and the components of multifractality in financial volatility. Chaos Solitons Fractals 45, 147–155 (2012)CrossRefGoogle Scholar
  52. W.X. Zhou, Z.H. Yu, Multifractality of drop breakup in the air-blast nozzle atomization process. Phys. Rev. E 63, 016302 (2001)CrossRefGoogle Scholar
  53. W.C. Zhou, H.C. Xu, Z.Y. Cai, J.R. Wei, X.Y. Zhu, W. Wang, L. Zhao, J.-P. Huang, Peculiar statistical properties of Chinese stock indices in bull and bear market phases. Phys. A 388, 891–899 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.NanjingChina
  2. 2.GuangzhouChina

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