Multifractal cross-correlation analysis based on statistical moments

Fractals

Volumn 20, Issue 3-4, 2012, Pages 271-279

  Wang, Jing ^a   Shang, Pengjian ^a   Ge, Weijie ^a  

^a BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Cross Correlations; Detrended Fluctuation Analysis; Multifractality; Statistical Moment; Time Series Analysis

Indexed keywords

CORRELATION METHODS; FRACTALS;

CROSS-CORRELATION ANALYSIS; CROSS-CORRELATIONS; DETRENDED CROSS-CORRELATIONS ANALYSIS; DETRENDED FLUCTUATION ANALYSIS; DETRENDING MOVING AVERAGES; MULTI FRACTALS; MULTIFRACTALITY; STATISTICAL MOMENTS; TIME-SERIES ANALYSIS; TIMES SERIES;

TIME SERIES ANALYSIS;

EID: 84871574748     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X12500259     Document Type: Article

References (47)

1. E. Bacry, J. Delour and J. F. Muzy, Multifractal random walk, Phys. Rev. E 64 (2001) 026103.
2. A. Arneodo, B. Audit, N. Decoster, J. F. Muzy and C. Vaillant, Wavelet Based Multifractal Formalism: Applications to DNA Sequences, Satellite Images of the Cloud Structure, and Stock Market Data (Springer, Berlin, 2002).
3. J. W. Kantelhardt, S. A. Zschiegner, A. Bunde, S. Havlin, E. Koscielny-Bunde and H. E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A 316 (2002) 87-114.
4. H.-O. Peitgen, H. Jurgens and D. Saupe, Chaos and Fractals (Springer, Berlin, 2004).
5. T. Di Matteo, Multi-scaling in finance, Quant. Financ. 7 (2007) 21-36.
6. G. F. Gu and W. X. Zhou, Detrendins moving average algorithm for multifractals, Phys. Rev. E 82 (2010).
7. R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics (Cambridge University Press, Cambridge, 2000).
8. Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng and H. E. Stanley, Statistical properties of the volatility of price fluctuations, Phys. Rev. E 60 (1999) 1390-1400.
9. N. Vandewalle, M. Ausloos and Ph. Boveroux, The moving averages demystified, Physica A 269 (1999) 170-176.
10. S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C.-K. Peng, M. Simons and H. E. Stanley, Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis, Phys. Rev. E 51 (1995) 5084-5091.
11. S. V. Buldyrev, N. V. Dokholyan, A. L. Goldberger, S. Havlin, C.-K. Peng, H. E. Stanley and G. M. Viswanathan, Analysis of DNA sequences using methods of statistical physics, Physica A 249 (1998) 430-438.
12. E. Koscielny-Bunde, A. Bunde, S. Havlin, H. E. Roman, Y. Goldreich and H.-J. Schellnhuber, Indication of a universal persistence law governing atmospheric variability, Phys. Rev. Lett. 81 (1998) 729-732.
13. P. Talkner and R. O. Weber, Power spectrum and detrended fluctuation analysis: application to daily temperatures, Phys. Rev. E 62 (2000) 150-160.
14. B. D. Malamud and D. L. Turcotte, Self-affine time series: measures of weak and strong persistence, J. Stat. Plan. Infer. 80 (1999) 173-196.
15. P. Ch. Ivanov, A. Bunde, L. A. N. Amaral, S. Havlin, J. Fritsch-Yelle, R. M. Baevsky, H. E. Stanley and A. L. Goldberger, Sleep-wake differences in scaling behavior of the human heartbeat: analysis of terrestrial and long-term space flight data, Europhys. Lett. 48 (1999) 594-560.
16. Y. Ashkenazy, P. Ch. Ivanov, S. Havlin, C.-K. Peng, A. L. Goldberger and H. E. Stanley, Magnitude and sign correlations in heartbeat fluctuations, Phys. Rev. Lett. 86 (2001) 1900-1903.
17. S. Bahar, J. W. Kantelhardt, A. Neiman, H. H. A. Rego, D. F. Russell, L. Wilkens, A. Bunde and F. Moss, Long-range temporal anti-correlations in paddlefish electroreceptors, Europhys. Lett. 56 (2001) 454-460.
18. P. Shang, Y. Lu and S. Kamae, Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis, Chaos Solitons Fractals 36 (2008) 82-90.
19. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley and A. L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685-1689.
20. A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J.-H. Peter and K. Voigt, Correlated and uncorrelated regions in heart-rate fluctuations during sleep, Phys. Rev. Lett. 85 (2000) 3736-3739.
21. C. Heneghan and G. McDarby, Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes, Phys. Rev. E 62 (2000) 6103-6110.
22. R. Weron, Estimating long-range dependence: finite sample properties and confidence intervals, Physica A 312 (2002) 285-299.
23. S. Arianos and A. Carbone, Detrending moving average algorithm: a closed-form approximation of the scaling law, Physica A 382 (2007) 9-15.
24. A.-L. Barabasi, P. Szepfalusy and T. Vicsek, Multifractal spectra of multi-affine functions, Physica A 178 (1991) 17-28.
25. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner and Y. Dodge, Turbulent cascades in foreign exchange markets, Nature 381 (1996) 767-770.
26. F. Schmitt, D. Schertzer and S. Lovejoy, Multifractal muctuations in finance, Int. J. Theoret. Appl. Fin. 3 (2000) 361-364.
27. J. Alvarez-Ramirez, M. Cisneros, C. Ibarra-Valdez and A. Soriano, Multifractal Hurst analysis of crude oil prices, Physica A 313 (2002) 651-670.
28. J. W. Lee, K. E. Lee and P. A. Rikvold, Multifractal behavior of the Korean stock-market index KOSPI, Physica A 364 (2006) 355-361.
29. 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, Physica A 316 (2002) 87-114.
30. X. Sun, H.-P. Chen, Y.-Z. Yuan and Z.-Q. Wu, Predictability of multifractal analysis of Hang Seng stock index in Hong Kong, Physica A 301 (2001) 473-482.
31. D.-S. Ho, C.-K. Lee, C.-C. Wang and M. Chuang, Scaling characteristics in the Taiwan stock market, Physica A 332 (2004) 448-460.
32. Z. Q. Jiang andW. X. Zhou, Multifractality in stock indexes: fact or fiction?, Physica A 387 (2008) 3605-3614.
33. A. Arneodo, E. Bacry, P. V. Graves and J. F. Muzy, Characterizing long-range correlations in DNA sequences from wavelet analysis, Phys. Rev. Lett. 74 (1995) 3293-3296.
34. M. Couillard and M. Davison, A comment on measuring the Hurst exponent of financial time series, Physica A 348 (2005) 404-418.
35. L. Xu, P. Ch. Ivanov, K. Hu, Z. Chen, A. Carbone and H. E. Stanley, Quantifying signals with powerlaw correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques, Phys. Rev. E 71 (2005) 051101.
36. A. Bashan, R. Bartsch, J. W. Kantelhardt and S. Havlin, Comparison of detrending methods for fluctuation analysis, Physica A 387 (2008) 5080-5090.
37. B. Podobnik and H. E. Stanley, Detrended crosscorrelation analysis: a new method for analyzing two nonstationary time series, Phys. Rev. Lett. 100 (2008) 084102.
38. W. X. Zhou, Multifractal detrended cross-correlation analysis for two nonstationary signals, Phys. Rev. E 77 (2008) 066211.
39. Z.-Q. Jiang and W.-X. Zhou, Multifractal detrending moving average cross-correlation analysis, Phys. Rev. E 84 (2011) 016106.
40. L. Kri?stoufek, Multifractal height cross-correlation analysis, research report, No. 2281, UTiA, Prague, Czech Republic (2010).
41. A.-L. Barabasi, P. Szepfalusy and T. Vicsek, Multifractal spectra of multi-affine functions, Physica A 178 (1991) 17-28.
42. J. M. Diego, E. Martinez-Gonzaalez, J. L. Sanz, S. Mollerach and V. J. Martinez, Partition function based analysis of cosmic microwave background maps, Mon. Not. R. Astron. Soc. 306 (1999) 427-436.
43. D.-S. Ho, C.-K. Lee, C.-C. Wang and M. Chuang, Scaling characteristics in the Taiwan stock market, Physica A 332 (2004) 448-460.
44. H. Zhang and K. Q. Dong, Muhifractal analysis of traffic flow time series, J. Hebei Univ. Eng. NA. 26 (2009) 109-112.
45. J. Feder, Fractals (Plenum Press, New York, 1988).
46. 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.
47. C. Meneveau and K. R. Sreenivasan, Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett. 59 (1987) 1424-1427.