Finite-size effect and the components of multifractality in financial volatility

Chaos, Solitons and Fractals

Volumn 45, Issue 2, 2012, Pages 147-155

  Zhou, Wei Xing ^a,b  

^a EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTALS; NORMAL DISTRIBUTION; TIME SERIES;

DOW JONES INDUSTRIAL AVERAGES; FINANCIAL VARIABLES; FINITE SIZE EFFECT; MULTIFRACTAL ANALYSIS; NON-LINEAR CORRELATIONS; NUMERICAL EXPERIMENTS; PARTITION FUNCTIONS; TEMPORAL CORRELATIONS;

SIZE DETERMINATION;

EID: 84855612750     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2011.11.004     Document Type: Article

References (83)

1. U. Frisch Turbulence: the legacy of A.N. Kolmogorov 1996 Cambridge University Press Cambridge
2. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge Turbulent cascades in foreign exchange markets Nature 381 1996 767 770 10.1038/381767a0 (Pubitemid 26243111)
3. R.N. Mantegna, and H.E. Stanley Turbulence and financial markets Nature 383 1996 587 588 10.1038/383587a0 (Pubitemid 26347573)
4. R.N. Mantegna, and H.E. Stanley Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena Phys A 239 1997 255 266 10.1016/S0378-4371(96)00484-0 (Pubitemid 127414401)
5. R.N. Mantegna, and H.E. Stanley An introduction to econophysics: correlations and complexity in finance 2000 Cambridge University Press Cambridge
6. B.B. Mandelbrot A multifractal walk down Wall Street Sci Am 298 1999 70 73 10.1038/scientificamerican0299-70
7. Z. Eisler, J. Kertész, S.-H. Yook, and A.-L. Barabási Multiscaling and non-universality in fluctuations of driven complex systems EPL (Europhys Lett) 69 2005 664 670 (Pubitemid 40317049)
8. Z. Eisler, and J. Kertész Liquidity and the multiscaling properties of the volume traded on the stock market EPL (Europhys Lett) 77 2007 28001
9. Z.-Q. Jiang, L. Guo, and W.-X. Zhou Endogenous and exogenous dynamics in the fluctuations of capital fluxes: an empirical analysis of the Chinese stock market Eur Phys J B 57 2007 347 355 10.1140/epjb/e2007-00174-7 (Pubitemid 47139310)
10. N. Vandewalle, and M. Ausloos Multi-affine analysis of typical currency exchange rates Eur Phys J B 4 1998 257 261 (Pubitemid 128437522)
11. K. Ivanova, and M. Ausloos Low q-moment multifractal analysis of Gold price, Dow Jones industrial average and BGL-USD exchange rate Eur Phys J B 8 1999 665 669 (Pubitemid 129558538)
12. F. Schmitt, D. Schertzer, and S. Lovejoy Multifractal analysis of foreign exchange data Appl Stoch Models Data Anal 15 1999 29 53
13. F. Schmitt, D. Schertzer, and S. Lovejoy Multifractal fluctuations in finance Int J Theoret Appl Financ 3 2000 361 364
14. L. Calvet, and A. Fisher Multifractality in asset returns: theory and evidence Rev Econ Stat 84 2002 381 406
15. M. Ausloos, and K. Ivanova Multifractal nature of stock exchange prices Comput Phys Commun 147 2002 582 585 (Pubitemid 34822777)
16. A.Z. Górski, S. Drod, and J. Speth Financial multifractality and its subtleties: an example of DAX Phys A 316 2002 496 510 (Pubitemid 35385263)
17. J. Alvarez-Ramirez, M. Cisneros, C. Ibarra-Valdez, and A. Soriano Multifractal Hurst analysis of crude oil prices Phys A 313 2002 651 670
18. M. Balcilar Multifractality of the Istanbul and Moscow stock market returns Emerg Markets Financ Trade 39 2 2003 5 46
19. K.E. Lee, and J.W. Lee Multifractality of the KOSPI in Korean stock market J Korean Phys Soc 46 2005 726 729
20. J.W. Lee, K.E. Lee, and P.A. Rikvold Multifractal behavior of the Korean stock-market index KOSPI Phys A 364 2006 355 361
21. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H.E. Stanley Multifractal detrended fluctuation analysis of nonstationary time series Phys A 316 2002 87 114 10.1016/S0378-4371(02)01383-3 (Pubitemid 35385237)
22. K. Matia, Y. Ashkenazy, and H.E. Stanley Multifractal properties of price fluctuations of stock and commodities EPL (Europhys Lett) 61 2003 422 428 (Pubitemid 36209155)
23. J. Kwapień, P. Oświȩcimka, and S. Drod Components of multifractality in high-frequency stock returns Phys A 350 2005 466 474 (Pubitemid 40338105)
24. K.E. Lee, and J.W. Lee Origin of the multifractality of the Korean stock-market index J Korean Phys Soc 47 2005 185 188 (Pubitemid 41273455)
25. P. Oświȩcimka, J. Kwapień, and S. Drod Multifractality in the stock market: price increments versus waiting times Phys A 347 2005 626 638
26. L.G. Moyana, J. de Souza, and S.M.D. Queiros Multi-fractal structure of traded volume in financial markers Phys A 371 2006 118 121
27. J. Jiang, K. Ma, and X. Cai Non-linear characteristics and long-range correlations in Asian stock markets Phys A 378 2007 399 407 10.1016/j.physa. 2006.12.011 (Pubitemid 46367498)
28. K.E. Lee, and J.W. Lee Probability distribution function and multiscaling properties in the Korean stock market Phys A 383 2007 65 70 10.1016/j.physa.2007.04.112 (Pubitemid 47016856)
29. G. Lim, S. Kim, H. Lee, K. Kim, and D.-I. Lee Multifractal detrended fluctuation analysis of derivative and spot markets Phys A 386 2007 259 266 10.1016/j.physa.2007.07.055 (Pubitemid 47539782)
30. Z.-Y. Su, Y.-T. Wang, and H.-Y. Huang A multifractal detrended fluctuation analysis of Taiwan's Stock Exchange J Korean Phys Soc 54 2009 1395 1402
31. G.-F. Gu, and W.-X. Zhou Detrending moving average algorithm for multifractals Phys Rev E 82 2010 011136 10.1103/PhysRevE.82.011136
32. X. Sun, H.-P. Chen, Z.-Q. Wu, and Y.-Z. Yuan Multifractal analysis of Hang Seng index in Hong Kong stock market Phys A 291 2001 553 562 (Pubitemid 32263031)
33. X. Sun, H.-P. Chen, Y.-Z. Yuan, and Z.-Q. Wu Predictability of multifractal analysis of Hang Seng stock index in Hong Kong Phys A 301 2001 473 482 (Pubitemid 33089180)
34. D.-S. Ho, C.-K. Lee, C.-C. Wang, and M. Chuang Scaling characteristics in the Taiwan stock market Phys A 332 2004 448 460
35. Y. Wei, and D.-S. Huang Multifractal analysis of SSEC in Chinese stock market: a different empirical result from Heng Seng Phys A 355 2005 497 508 (Pubitemid 40940863)
36. G.-F. Gu, W. Chen, and W.-X. Zhou Quantifying bid-ask spreads in the Chinese stock market using limit-order book data: intraday pattern, probability distribution, long memory, and multifractal nature Eur Phys J B 57 2007 81 87 10.1140/epjb/e2007-00158-7 (Pubitemid 46870961)
37. G.-X. Du, and X.-X. Ning Multifractal properties of Chinese stock market in Shanghai Phys A 387 2008 261 269
38. X.-T. Zhuang, and Y. Yuan Multifractal description of stock price index fluctuation using a quadratic function fitting Phys A 387 2008 511 518 10.1016/j.physa.2007.09.015 (Pubitemid 350166119)
39. Y. Wei, and P. Wang Forecasting volatility of SSEC in Chinese stock market using multifractal analysis Phys A 387 2008 1585 1592 10.1016/j.physa.2007.11.015 (Pubitemid 50015415)
40. W.-X. Zhou Illusionary multifractality in high-frequency data of Shanghai Stock Exchange Composite Index (in Chinese) J Manag Sci China 13 2010 81 86 (in Chinese)
41. Z.-Q. Jiang, and W.-X. Zhou Multifractality in stock indexes: Fact or Fiction? Phys A 387 2008 3605 3614 10.1016/j.physa.2008.02.015
42. Z.-Y. Su, and Y.-T. Wang An investigation into the multifractal characteristics of the TAIEX stock exchange index in Taiwan J Korean Phys Soc 54 2009 1385 1394
43. Z.-Q. Jiang, and W.-X. Zhou Scale invariant distribution and multifractality of volatility multiplier in stock markets Phys A 381 2007 343 350 10.1016/j.physa.2007.03.015 (Pubitemid 46829653)
44. Z.R. Struzik, and A.P.J.M. Siebes Wavelet transform based multifractal formalism in outlier detection and localisation for financial time series Phys A 309 2002 388 402 (Pubitemid 34614327)
45. A. Turiel, and C.J. Pérez-Vicente Multifractal geometry in stock market time series Phys A 322 2003 629 649
46. A. Turiel, and C.J. Pérez-Vicente Role of multifractal sources in the analysis of stock market time series Phys A 355 2005 475 496 (Pubitemid 40940862)
47. P. Oświȩcimka, J. Kwapień, S. Drod, and R. Rak Investigating multifractality of stock market fluctuations using wavelet and detrending fluctuation methods Acta Phys Pol B 36 2005 2447 2457
48. A. Turiel, and N. Parga The multifractal structure of contrast changes in natural images: from sharp edges to textures Neural Comput 12 2000 763 793 10.1162/089976600300015583
49. A. Turiel, and A. del Pozo Reconstructing images from their most singular fractal manifold IEEE Trans Image Proc 11 2002 345 350 10.1109/TIP.2002.999668 (Pubitemid 34692385)
50. O. Pont, A. Turiel, and C.J. Perez-Vicente Application of the microcanonical multifractal formalism to monofractal systems Phys Rev E 74 2006 061110 10.1103/PhysRevE.74.061110 (Pubitemid 44925332)
51. A. Turiel, C.J. Perez-Vicente, and J. Grazzini Numerical methods for the estimation of multifractal singularity spectra on sampled data: a comparative study J Comput Phys 216 2006 362 390 10.1016/j.jcp.2005.12.004 (Pubitemid 44307899)
52. A. Turiel, H. Yahia, and C.J. Perez-Vicente Microcanonical multifractal formalism - A geometrical approach to multifractal systems: Part I. Singularity analysis J Phys A: Math Theor 41 2008 01550 10.1088/1751-8113/41/1/015501
53. O. Pont, A. Turiel, and C.J. Perez-Vicente Empirical evidences of a common multifractal signature in economic, biological and physical systems Phys A 388 2009 2025 2035 10.1016/j.physa.2009.01.041
54. L. Zunino, B.M. Tabak, A. Figliola, D.G. Pérez, M. Garavaglia, and O.A. Rosso A multifractal approach for stock market inefficiency Phys A 387 2008 6558 6566 10.1016/j.physa.2008.08.028
55. L. Zunino, A. Figliola, B.M. Tabak, D.G. Pérez, M. Garavaglia, and O.A. Rosso Multifractal structure in Latin-American market indices Chaos, Solitons Fractals 41 2009 2331 2340 10.1016/j.chaos.2008.09.013
56. Y.-D. Wang, L. Liu, and R.-B. Gu Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis Int Rev Financ Anal 18 2009 271 276 10.1016/j.irfa.2009.09.005
57. J.-P. Bouchaud, M. Potters, and M. Meyer Apparent multifractality in financial time series Eur Phys J B 13 2000 595 599
58. A. Saichev, and D. Sornette Generic multifractality in exponentials of long memory processes Phys Rev E 74 2006 011111
59. T. Lux Detecting multifractal properties in asset returns: the failure of the "scaling estimator" Int J Modern Phys C 15 2004 481 491 (Pubitemid 40262498)
60. W.-X. Zhou The components of empirical multifractality in financial returns EPL (Europhys Lett) 88 2009 28004 10.1209/0295-5075/88/28004
61. J. de Souza, and S.M.D. Queirós Effective multifractal features of high-frequency price fluctuations time series and ℓ-variability diagrams Chaos, Solitons Fractals 42 2009 2512 2521 10.1016/j.chaos.2009.03.198
62. H. Jin, and J.-Z. Lu Origins of the multifractality in Shanghai stock market Il Nuovo Cimento B 121 2006 987 994 10.1393/ncb/i2007-10026-3
63. S. Kumar, and N. Deo Multifractal propertirs of the Indian financial market Phys A 388 2009 1593 1602 10.1016/j.physa.2008.12.017
64. G. Oh, C. Eom, S. Havlin, W.-S. Jung, F.-Z. Wang, and H.E. Stanley Effect of Asian currency crisis on multifractal spectra 2008 arXiv: 0801.1475
65. P. Norouzzadeh, and B. Rahmani A multifractal detrended fluctuation description of Iranian rial-US dollar exchange rate Phys A 367 2006 328 336 10.1016/j.physa.2005.11.019 (Pubitemid 43674297)
66. P. Cizeau, Y.-H. Liu, M. Meyer, C.-K. Peng, and H.E. Stanley Volatility distribution in the S& P 500 stock index Phys A 245 1997 441 445 (Pubitemid 127396407)
67. M. Pasquini, and M. Serva Clustering of volatility as a multiscale phenomenon Eur Phys J B 16 2000 195 201
68. B. Bollen, and B. Inder Estimating daily volatility in financial markets utilizing intraday data J Emp Financ 9 2002 551 562 10.1016/S0927-5398(02)00010- 5
69. T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman Fractal measures and their singularities: the characterization of strange sets Phys Rev A 33 1986 1141 1151
70. J. von Hardenberg, R. Thieberger, and A. Provenzale A box-counting red herring Phys Lett A 269 2000 303 308 10.1016/S0375-9601(00)00265-6
71. H. Nakao Multi-scaling properties of truncated Lévy flights Phys Lett A 266 2000 282 289
72. S. Drod, J. Kwapień, P. Oświecimka, and R. Rak Quantitative features of multifractal subtleties in time series EPL (Europhys Lett) 88 2009 60003 10.1209/0295-5075/88/60003
73. P.L. Hsu, and H. Robbins Complete convergence and the law of large numbers Proc Natl Acad Sci USA 33 1947 25 31
74. Mandelbrot BB, Fisher AJ, Calvet LE. A multifractal model of asset returns, cowles Foundation Discussion Paper No. 1164, 1997.
75. Z.-X. Ding, and C.W.J. Granger Modeling volatility persistence of speculative returns: a new approach J Emp Financ 73 1993 185 215
76. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery Numerical recipes in FORTRAN: the art of scientific computing 1996 Cambridge University Press Cambridge
77. T. Schreiber, and A. Schmitz Improved surrogate data for nonlinearity tests Phys Rev Lett 77 1996 635 638 10.1103/PhysRevLett.77.635 (Pubitemid 126624517)
78. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J.D. Farmer Testing for nonlinearity in time series: the method of surrogate data Phys D 58 1992 77 94 10.1016/0167-2789(92)90102-S
79. M.I. Bogachev, J.F. Eichner, and A. Bunde Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets Phys Rev Lett 99 2007 240601 10.1103/PhysRevLett.99.240601 (Pubitemid 350243211)
80. P. Gopikrishnan, M. Meyer, L.A.N. Amaral, and H.E. Stanley Inverse cubic law for the distribution of stock price variations Eur Phys J B 3 1998 139 140 (Pubitemid 128437570)
81. Y. Malevergne, and D. Sornette Extreme financial risks: from dependence to risk management 2006 Springer Berlin
82. P.C. Ivanov, L.A.N. Amaral, A.L. Goldberger, S. Havlin, M.G. Rosenblum, and Z.R. Struzik Multifractality in human heartbeat dynamics Nature 399 1999 461 465 10.1038/20924 (Pubitemid 29258850)
83. P.C. Ivanov, L.A.N. Amaral, A.L. Goldberger, S. Havlin, M.G. Rosenblum, and H.E. Stanley From 1/f noise to multifractal cascades in heartbeat dynamics Chaos 11 2001 641 652 10.1063/1.1395631