Global and Local Approaches Describing Critical Phenomena on the Developing and Developed Financial Markets

  • Dariusz Grech


We define and confront global and local methods to analyze the financial crash-like events on the financial markets from the critical phenomena point of view. These methods are based respectively on the analysis of log-periodicity and on the local fractal properties of financial time series in the vicinity of phase transitions (crashes). The log-periodicity analysis is made in a daily time horizon, for the whole history (1991–2008) of Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. We find that crash-like events on the Polish financial market are described better by the log-divergent price model decorated with log-periodic behavior than by the power-law-divergent price model usually discussed in log-periodic scenarios for developed markets. Predictions coming from log-periodicity scenario are verified for all main crashes that took place in WIG history. It is argued that crash predictions within log-periodicity model strongly depend on the amount of data taken to make a fit and therefore are likely to contain huge inaccuracies. Next, this global analysis is confronted with the local fractal description. To do so, we provide calculation of the so-called local (time dependent) Hurst exponent H loc for the WIG time series and for main US stock market indices like DJIA and S&P 500. We point out dependence between the behavior of the local fractal properties of financial time series and the crashes appearance on the financial markets. We conclude that local fractal method seems to work better than the global approach – both for developing and developed markets. The very recent situation on the market, particularly related to the Fed intervention in September 2007 and the situation immediately afterwards is also analyzed within fractal approach. It is shown in this context how the financial market evolves through different phases of fractional Brownian motion. Finally, the current situation on American market is analyzed in fractal language. This is to show how far we still are from the end of recession and from the beginning of a new boom on US financial market or on other world leading stocks.


Stock Market Financial Market Hurst Exponent Detrended Fluctuation Analysis Financial Time Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Author wishes to thank Ewa Sochocka for her outstanding support and encouragement he experienced preparing this article.


  1. 1.
    Mandelbrot BB (1963) J Business 36:349Google Scholar
  2. 2.
    Sornette D, Johansen A, Bouchaud J-P (1996) J Phys I (France) 6:167CrossRefGoogle Scholar
  3. 3.
    Feigenbaum JA, Freund PGO (1996) Int J Mod Phys B 10:3737ADSCrossRefMATHGoogle Scholar
  4. 4.
    Takayasu H, Miura H, Hirabayashi T, Hamada K (1992) Physica A 184:127ADSCrossRefGoogle Scholar
  5. 5.
    Bouchaud J-P, Sornette D (1994) J Phys I (France) 4:863CrossRefMATHGoogle Scholar
  6. 6.
    Mantegna RN, Stanley HE (1995) Nature 376:46ADSCrossRefGoogle Scholar
  7. 7.
    Liu Y, Cizeau P, Meyer M, Peng C-K, Stanley HE (1997) Physica A 245:437MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Bak P, Paczuski M, Shubik M (1997) Physica A 246:430ADSCrossRefGoogle Scholar
  9. 9.
    Sornette D, Johansen A (1997) Physica A 245:411MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Vandewalle N, Boveroux Ph, Minguet A, Ausloos M (1998) Physica A 255:201CrossRefGoogle Scholar
  11. 11.
    Vandewalle N, Ausloos M, Boveroux Ph, Minguet A (1998) Eur Phys J B 4:139ADSCrossRefGoogle Scholar
  12. 12.
    Vandewalle N, Ausloos M, Boveroux Ph, Minguet A (1999) Eur Phys J B 9:355ADSCrossRefGoogle Scholar
  13. 13.
    Johansen A, Sornette D (2000) Eur Phys J B 17:319ADSCrossRefGoogle Scholar
  14. 14.
    Ausloos M, Ivanova K, Vandewalle N (2002) Crashes: symptoms, diagnoses and remedies. In: Takayasu H (ed) Empirical sciences of finacial fluctuations. The advent of econophysics. Tokyo, Japan, Nov. 15–17, 2000 Proceedings. Springer, Berlin, pp 62–76 (arXiv: cond-mat/0104127)Google Scholar
  15. 15.
    Drożdż S, Grummer F, Ruf F, Speth J (2003) Physica A 324:174ADSCrossRefMATHGoogle Scholar
  16. 16.
    Grech D, Mazur Z (2004) Physica A 336:133ADSCrossRefGoogle Scholar
  17. 17.
    Bartolozzi M, Drożdż S, Leinweber DB, Speth J, Thomas AW (2005) Int J Mod Phys C 16:1347ADSCrossRefGoogle Scholar
  18. 18.
    Sornette D (1998) Phys Rep 297:239MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Drożdż S, Ruf F, Speth J, Wójcik M (1999) Eur Phys J B 10:589ADSCrossRefGoogle Scholar
  20. 20.
    Kozłowska M, Kasprzak A, Kutner R (2008) Int J Mod Phys C 19:453ADSCrossRefMATHGoogle Scholar
  21. 21.
    Hurst HE (1951) Trans Am Soc Civ Eng 116:770Google Scholar
  22. 22.
    Mandelbrot BB, Wallis JR (1969) Water Resour Res 5(2):321ADSCrossRefGoogle Scholar
  23. 23.
    Peng C-K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Golberger AL (1994) Phys Rev E 49:1685ADSCrossRefGoogle Scholar
  24. 24.
    Allesio E, Carbone A, Castelli G, Frappietro V (2002) Eur Phys J B 27:197ADSGoogle Scholar
  25. 25.
    Carbone A, Castelli G (2003) Proc SPIE 5114:407ADSGoogle Scholar
  26. 26.
    Geweke J, Porter-Hudak S (1983) Jour Time Ser Anal 4:221MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Vandewalle N, Ausloos M (1997) Physica A 246:454ADSCrossRefGoogle Scholar
  28. 28.
    Ausloos M, Vandewalle N, Boveroux Ph, Minguet A, Ivanova K (1999) Physica A 274:229ADSCrossRefGoogle Scholar
  29. 29.
    Viswanathan GM, Peng C-K, Stanley HE, Goldberger AL (1997) Phys Rev E 55:845ADSCrossRefGoogle Scholar
  30. 30.
    Kantelhardt JW, Koscielny-Bunde E, Rego HHA, Havlin S, Bunde A (2001) Physica A 295:441ADSCrossRefMATHGoogle Scholar
  31. 31.
    Hu K, Ivanov PCh, Chen Z, Carpena P, Stanley HE (2001) Phys Rev E 64:011114ADSCrossRefGoogle Scholar
  32. 32.
    Chen Z, Ivanov PCh, Hu K, Stanley HE (2002) Phys Rev E 65:041107ADSCrossRefGoogle Scholar
  33. 33.
    Chen Z, Hu K, Carpena P, Bernaola-Galvan P, Stanley HE, Ivanov PCh (2005) Phys Rev E 71:011104ADSCrossRefGoogle Scholar
  34. 34.
    Buldyrev SV, Dokholyan NV, Golberger AL, Havlin S, Peng C-K, Stanley HE, Viswanathan GM (1998) Physica A 249:430CrossRefGoogle Scholar
  35. 35.
    Moret MA, Zebenda GF, Nogueira E, Pereira MG (2003) Phys Rev E 68:041104ADSCrossRefGoogle Scholar
  36. 36.
    Vandewalle N, Ausloos M (1998) Phys Rev E 58:6832ADSCrossRefGoogle Scholar
  37. 37.
    Ausloos M, Ivanova K (2001) Int J Mod Phys C 12:169CrossRefGoogle Scholar
  38. 38.
    Ausloos M, Ivanova K (2000) Physica A 286:353ADSCrossRefMATHGoogle Scholar
  39. 39.
    Ausloos M, Ivanova K (2001) Eur Phys J B 20:537ADSCrossRefGoogle Scholar
  40. 40.
    Oświȩcimka P, Kwapień J, Drożdż S, Rak R (2005) Acta Phys Pol B 36:2447ADSGoogle Scholar
  41. 41.
    Czarnecki L, Grech D, Pamuła G (2008) Physica A 387:6801ADSCrossRefGoogle Scholar
  42. 42.
    Grech D, Pamuła G (2008) Physica A 387:4299ADSCrossRefGoogle Scholar
  43. 43.
    Drożdż S, Kwapień J, Oświȩcimka P, Speth J (2008) Acta Phys Pol A 114:539. arXiv: 0802.4043v1 [physics.soc-ph]ADSGoogle Scholar
  44. 44.
    Carbone A, Castelli G, Stanley HE (2004) Physica A 344:267MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Cajueiro DO, Tabak BM (2004) Physica A 336:521MathSciNetADSCrossRefGoogle Scholar
  46. 46.
    Eom C, Choi S, Oh G, Jung W-S (2008) Physica A 387:4630ADSCrossRefGoogle Scholar
  47. 47.
    Eom C, Oh G, Jung W-S (2008) Physica A 387:5511ADSCrossRefGoogle Scholar

Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsUniversity of WrocławWrocławPoland

Personalised recommendations