PL EN


Preferences help
enabled [disable] Abstract
Number of results
2013 | 123 | 3 | 529-537
Article title

Multifractality of Nonlinear Transformations with Application in Finances

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
We study the multifractal effects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the "true" unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A difference is stressed between "naive" observed multifractal effects calculated directly within detrended multifractal analysis as the spread Δh of the generalized Hurst exponents h(q) and the more reliable unbiased multifractality received after subtraction of residual bias effects generated by nonlinear transformations of initial data and coupled with finite size effects in time series. This property is investigated for volatile series of the real main world financial indices. A difference between multifractal properties of intraday and interday quotes is also pointed out in this context for the Warsaw Stock Exchange WIG index. Finally, based on the observed feature of real nonstationary data, a new measure of unbiased multifractality in signals is introduced. This measure comes from an analysis of the whole generalized Hurst exponent profile instead of looking just at its edge behavior h^{±} ≡ h(q→ ±∞). Such an approach seems to be particularly useful when h(q) is not a monotonic function of the moment order q. Interesting examples with extreme events from finance are presented. They convince that an analysis directed only on investigation of the edges h^{±} in multifractal spectrum may be misleading.
Keywords
Year
Volume
123
Issue
3
Pages
529-537
Physical description
Dates
published
2013-03
References
  • [1] M.S. Taqqu, V. Teverovsky, W. Willinger, doi: 10.1142/S0218348X95000692, Fractals 3, 785 (1995)
  • [2] Fractals in Science, Eds. A. Bunde, S. Havlin, 2nd ed., Springer, Berlin 1996
  • [3] H.E. Hurst, Trans. Am. Soc. Civ. Eng. 116, 770 (1951)
  • [4] B.B. Mandelbrot, J.R. Wallis, Water Resour. Res. 5, 321 (1969)
  • [5] J.W. Kantelhardt, E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, doi: 10.1016/S0378-4371(01)00144-3, Physica A 295, 441 (2001)
  • [6] J.W. Kantelhardt, in: Encyclopedia of Complexity and Systems Science, Ed. R.A. Meyers, Springer, Berlin 2009, p. 3754
  • [7] J.F. Muzy, E. Bacry, A. Arneodo, doi: 10.1103/PhysRevLett.67.3515, Phys. Rev. Lett. 67, 3515 (1991)
  • [8] J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley, doi: 10.1016/S0378-4371(02)01383-3, Physica A 316, 87 (2002)
  • [9] C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, doi: 10.1103/PhysRevE.49.1685, Phys. Rev. E 49, 1685 (1994)
  • [10] C.-K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, doi: 10.1063/1.166141, Chaos 5, 82 (1995)
  • [11] P. Oświęcimka, J. Kwapień, S. Drożdż, doi: 10.1103/PhysRevE.74.016103, Phys. Rev. E 74, 016103 (2006)
  • [12] L. Telesca, V. Lapenna, M. Macchiato, doi: 10.1016/j.physa.2005.02.053, Physica A 354, 629 (2005)
  • [13] L. Telesca, V. Lapenna, doi: 10.1016/j.tecto.2006.03.023, Tectonophysics 423, 115 (2006)
  • [14] M.S. Movahed, F. Ghasemi, S. Rahvar, M.R.R. Tabar, doi: 10.1103/PhysRevE.84.021103, Phys. Rev. E 84, 021103 (2011)
  • [15] P.H. Figueiredo, E. Nogueira Jr., M.A. Moret, S. Coutinho, doi: 10.1016/j.physa.2009.11.045, Physica A 389, 2090 (2010)
  • [16] S. Dutta, doi: 10.1088/1742-5468/2010/12/P12021, J. Stat. Mech. 12, P12021 (2010)
  • [17] I.T. Pedron, doi: 10.1088/1742-6596/246/1/012034, J. Phys. Conf. Series 246, 012034 (2010)
  • [18] F. Liao, Y.-K. Jan, doi: 10.1682/JRRD.2010.08.0145, J. Rehab. Res. Develop. 48, 787 (2011)
  • [19] Y. Leung, E. Ge, Z. Yu, doi: 10.1080/00045608.2011.592733, Ann. Assoc. Am. Geograph. 101, 1221 (2011)
  • [20] G.R. Jafari, P. Pedram, L. Hedayatifar, doi: 10.1088/1742-5468/2007/04/P04012, J. Stat. Mech., P04012 (2007)
  • [21] P. Oświęcimka, J. Kwapień, I. Celińska, S. Drożdż, R. Rak, arxiv/1106.2902v1 [physics.data-an]
  • [22] F.A. Hirpa, M. Gebremichael, T.M. Over, doi: 10.1029/2009WR009000, Water Resour. Res. 46, W12529 (2010)
  • [23] M. Pasquini, M. Serva, doi: 10.1016/S0165-1765(99)00159-7, Econ. Lett. 65, 275 (1999)
  • [24] K. Ivanova, M. Ausloos, doi: 10.1016/S0378-4371(98)00562-7, Physica A 265, 279 (1999)
  • [25] A. Bershadskii, doi: 10.1007/s100510050945, Eur. Phys. J. B 11, 361 (1999)
  • [26] N. Vandewalle, M. Ausloos, doi: 10.1007/s100510050376, Eur. Phys. J. B 4, 257 (1998)
  • [27] A. Bershadskii, doi: 10.1016/S0378-4371(02)01339-0, Physica A 317, 591 (2003)
  • [28] T. Di Matteo, T. Aste, M.M. Dacorogna, doi: 10.1016/S0378-4371(02)01996-9, Physica A 324, 183 (2003)
  • [29] K. Matia, Y. Ashkenazy, H.E. Stanley, doi: 10.1209/epl/i2003-00194-y, Europhys. Lett. 61, 422 (2003)
  • [30] P. Oświęcimka, J. Kwapień, S. Drożdż, doi: 10.1016/j.physa.2004.08.025, Physica A 347, 626 (2005)
  • [31] J. Kwapień, P. Oświęcimka, S. Drożdż, doi: 10.1016/j.physa.2004.11.019, Physica A 350, 466 (2005)
  • [32] Z. Chen, P.Ch. Ivanov, K. Hu, H.E. Stanley, doi: 10.1016/S0378-4371(02)01383-3, Phys. Rev. E 65, 041107 (2002)
  • [33] D. Grech, G. Pamuła, Acta Phys. Pol. A 121, B34 (2012)
  • [34] D. Grech, G. Pamuła, arxiv/1108.1951v2
  • [35] G. Pamula, D. Grech, in preparation
  • [36] S. Drożdż, J. Kwapień, P. Oświęcimka, R. Rak, doi: 10.1209/0295-5075/88/60003, Europhys. Lett. 88, 60003 (2009), arxiv/0907.2866 [physics.data-an]
  • [37] Wei-Xing Zhou, arxiv/0912.4782v [q-fin.ST]
  • [38] J. Ludescher, M.I. Bogachev, J.W. Kantelhardt, A.Y. Schumann, A. Bunde, doi: 10.1016/j.physa.2011.03.008, Physica A 390, 2480 (2011)
  • [39] A.Y. Schumann, J.W. Kantelhardt, doi: 10.1016/j.physa.2011.03.002, Physica A 390, 2637 (2011)
  • [40] D. Gulich, L. Zunino, doi: 10.1016/j.physa.2012.04.001, Physica A 391, 4100 (2012)
  • [41] T. Kalisky, Y. Ashkenazy, S. Havlin, doi: 10.1103/PhysRevE.72.011913, Phys. Rev. E 72, 011913 (2005)
  • [42] H.A. Makse, S. Havlin, M. Schwartz, H.E. Stanley, doi: 10.1103/PhysRevE.53.5445, Phys. Rev. E 53, 5445 (1996)
  • [43] J. Feder, Fractals, Plenum Press, New York 1988
  • [44] R.C. Altman, 'The Great Crash 2008', Foreign Affairs, (Jan./Feb. 2009), p. 1
  • [45] G.M. Hodgson, Cambr. J. Econ. 33, 10205 (2009)
  • [46] N. Vandewalle, M. Ausloos, Ph. Boveroux, A. Minguet, doi: 10.1007/s100510050775, Eur. Phys. J. B 9, 355 (1999)
  • [47] D. Sornette, R. Woodard, Wei-Xing Zhou, doi: 10.1016/j.physa.2009.01.01110.1016/j.physa.2009.01.011, Physica A 388, 8 (2009)
  • [48] Ł. Carnecki, D. Grech, G. Pamuła, doi: 10.1016/j.physa.2008.08.019, Physica A 387, 6801 (2008)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv123n308kz
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.