Scale invariant distribution and multifractality of volatility multipliers in stock markets

Physica A: Statistical Mechanics and its Applications

Volumn 381, Issue 1-2, 2007, Pages 343-350

  Jiang, Zhi Qiang ^a   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

Econophysics; Multifractal analysis; Multiplier; Scale invariance; Stock markets; Volatility

Indexed keywords

DATA ACQUISITION; FINANCE; NORMAL DISTRIBUTION; STATISTICAL METHODS;

MULTIFRACTALITY; SCALE INVARIANT DISTRIBUTION; STOCK MARKETS; VOLATILITY MULTIPLIERS;

MARKETING;

EID: 34249735899     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.03.015     Document Type: Article

References (50)

1. L. Bachelier, Théorie de la Spéculation, Ph.D. thesis, University of Paris, Paris, March 29, 1990.
2. Mandelbrot B.B. Fractals and Scaling in Finance (1997), Springer, New York
3. Mantegna R.N., and Stanley H.E. Scaling behaviour in the dynamics of an economic index. Nature 376 (1995) 46-49
4. Ghashghaie S., Breymann W., Peinke J., Talkner P., and Dodge Y. Turbulent cascades in foreign exchange markets. Nature 381 (1996) 767-770
5. Mantegna R.N., and Stanley H.E. Turbulence and financial markets. Nature 383 (1996) 587-588
6. Vandewalle N., and Ausloos M. Sparseness and roughness of foreign exchange rates. Int. J. Mod. Phys. C 9 (1998) 711-719
7. Schmitt F., Schertzer D., and Lovejoy S. Multifractal analysis of foreign exchange data. Appl. Stochast. Models Data Anal. 15 (1999) 29-53
8. Ivanova K., and Ausloos M. 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
9. Baviera R., Pasquini M., Serva M., Vergni D., and Vulpiani A. Correlations and multi-affinity in high frequency financial datasets. Physica A 300 (2001) 551-557
10. Muniandy S.V., Lim S.C., and Murugan R. Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates. Physica A 301 (2001) 407-428
11. Xu Z.-X., and Gençay R. Scaling, self-similarity and multifractality in FX markets. Physica A 323 (2003) 578-590
12. Matia K., Ashkenazy Y., and Stanley H.E. Multifractal properties of price fluctuations of stock and commodities. Europhys. Lett. 61 (2003) 422-428
13. Turiel A., and Pérez-Vicente C.J. Multifractal geometry in stock market time series. Physica A 322 (2003) 629-649
14. Oświȩcimka P., Kwapień J., Drożdż S., and Rak R. Investigating multifractality of stock market fluctuations using wavelet and detrending fluctuation methods. Acta Phys. Polon. B 36 (2005) 2447-2457
15. Olsen L. Multifractal geometry. Progr. Prob. 46 (2000) 3-37
16. Turiel A., and Pérez-Vicente C.J. Role of multifractal sources in the analysis of stock market time series. Physica A 355 (2005) 475-496
17. Norouzzadeh P., and Jafari G.R. Application of multifractal measures to Tehran price index. Physica A 356 (2005) 609-627
18. Bershadskii A. Multifractal diffusion in NASDAQ. J. Phys. A 34 (2001) L127-L130
19. Sun X., Chen H.-P., Wu Z.-Q., and Yuan Y.-Z. Multifractal analysis of Hang Seng index in Hong Kong stock market. Physica A 291 (2001) 553-562
20. Sun X., Chen H.-P., Yuan Y.-Z., and Wu Z.-Q. Predictability of multifractal analysis of Hang Seng stock index in Hong Kong. Physica A 301 (2001) 473-482
21. Andreadis I., and Serletis A. Evidence of a random multifractal turbulent structure in the Dow Jones Industrial Average. Chaos, Solitons and Fractals 13 (2002) 1309-1315
22. Górski A.Z., Drożdż S., and Speth J. Financial multifractality and its subtleties: an example of DAX. Physica A 316 (2002) 496-510
23. Ausloos M., and Ivanova K. Multifractal nature of stock exchange prices. Comput. Phys. Commun. 147 (2002) 582-585
24. Balcilar M. Multifractality of the Istanbul and Moscow stock market returns. Emerging Markets Fin. Trade 39 2 (2003) 5-46
25. Lee K.E., and Lee J.W. Multifractality of the KOSPI in Korean stock market. J. Korean Phys. Soc. 46 (2005) 726-729
26. Lee K.E., and Lee J.W. Origin of the multifractality of the Korean stock-market index. J. Korean Phys. Soc. 47 (2005) 185-188
27. Lee J.W., Lee K.E., and Pikvold P.A. Multifractal behavior of the Korean stock-market index KOSPI. Physica A 364 (2006) 355-361
28. Wei Y., and Huang D.-S. Multifractal analysis of SSEC in Chinese stock market: a different empirical result from Heng Seng. Physica A 355 (2005) 497-508
29. Holschneider M. On the wavelet transformation of fractal objects. J. Stat. Phys. 50 (1988) 953-993
30. Muzy J.-F., Bacry E., and Arnéodo A. Wavelets and multifractal formalism for singular signals: application to turbulence data. Phys. Rev. Lett. 67 (1991) 3515-3518
31. Muzy J.-F., Bacry E., and Arnéodo A. Multifractal formalism for fractal signals: the structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E 47 (1993) 875-884
32. Kantelhardt J.W., Zschiegner S.A., Koscielny-Bunde E., Havlin S., Bunde A., and Stanley H.E. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316 (2002) 87-114
33. Saichev A., and Sornette D. Generic multifractality in exponentials of long memory processes. Phys. Rev. E 74 (2006) 011111
34. Lux T. Detecting multifractal properties in asset returns: the failure of the scaling estimator. Int. J. Mod. Phys. C 15 (2004) 481-491
35. Chhabra A.B., and Sreenivasan K.R. Negative dimensions: theory, computation and experiment. Phys. Rev. A 43 (1991) 1114-1117
36. Chhabra A.B., and Sreenivasan K.R. Scale-invariant multiplier distribution in turbulence. Phys. Rev. Lett. 68 (1992) 2762-2765
37. Jouault B., Lipa P., and Greiner M. Multiplier phenomenology in random multiplicative cascade processes. Phys. Rev. E 59 (1999) 2451-2454
38. Jouault B., Greiner M., and Lipa P. Fix-point multiplier distributions in discrete turbulent cascade models. Physica D 136 (2000) 125-144
39. Novikov E.A. Intermittency and scale similarity in the structure of a turbulent flow. J. Appl. Math. Mech. 35 (1971) 231-241
40. Bollen B., and Inder B. Estimating daily volatility in financial markets utilizing intraday data. J. Emp. Fin. 9 (2002) 551-562
41. Molenaar J., Herweijer J., and van de Water W. Negative dimensions of the turbulent dissipation field. Phys. Rev. E 52 (1995) 496-509
42. Kluiving R., and Pasmanter R.A. Stochastic selfsimilar branching and turbulence. Physica A 228 (1996) 273-294
43. Gluzman S., and Sornette D. Log-periodic route to fractal functions. Phys. Rev. E 65 (2002) 036142
44. Zhou W.-X., and Yu Z.-H. On the properties of random multiplicative measures with the multipliers exponentially distributed. Physica A 294 (2001) 273-282
45. Zhou W.-X., Liu H.-F., and Yu Z.-H. Anormalous features arising from random multifractals. Fractals 9 (2001) 317-328
46. Zhou W.-X., and Yu Z.-H. Multifractality of drop breakup in the air-blast nozzle atomization process. Phys. Rev. E 63 (2001) 016302
47. L'vov V.S., Podivilov E., Pomyalov A., Procaccia I., and Vandembroucq D. Improved shell model of turbulence. Phys. Rev. E 58 (1998) 1811-1822
48. Zhou W.-X., Sornette D., and Yuan W.-K. Inverse statistics and multifractality of exit distances in 3D fully developed turbulence. Physica D 214 (2006) 55-62
49. Pearson B.R., and van de Water W. Inverse structure functions. Phys. Rev. E 71 (2005) 036303
50. Mandelbrot B.B. Negative fractal dimensions and multifractals. Physica A 163 (1990) 306-315