Eliminating finite-size effects and detecting the amount of white noise in short records with long-term memory

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 6, 2009, Pages

  Lennartz, Sabine ^a   Bunde, Armin ^a  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADDITIVE WHITE NOISE; AUTOCORRELATION FUNCTIONS; CORRELATED DATA; CORRELATION EXPONENTS; DATA SETS; FINITE SIZE EFFECT; GAUSSIAN DISTRIBUTED; LOCAL MEAN; LONG TERM MEMORY; NATURAL HAZARD; SIZE PARAMETERS; TIME WINDOWS;

BARIUM; REGRESSION ANALYSIS;

WHITE NOISE;

EID: 67650912363     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.066101     Document Type: Article

References (23)

1. B. B. Mandelbrot and J. R. Wallis, Water Resour. Res. 5, 321 (1969). 10.1029/WR005i002p00321
2. Y. Ashkenazy, D. R. Baker, H. Gildor, and S. Havlin, Geophys. Res. Lett. 30, 2146 (2003). 10.1029/2003GL018099
3. E. Koscielny-Bunde, A. Bunde, S. Havlin, and Y. Goldreich, Physica A 231, 393 (1996). 10.1016/0378-4371(96)00187-2
4. J. D. Pelletier and D. L. Turcotte, J. Hydrol. 203, 198 (1997) 10.1016/S0022-1694(97)00102-9
5. J. D. Pelletier and D. L. Turcotte, Adv. Geophys. 40, 91 (1999).
6. E. Koscielny-Bunde, A. Bunde, S. Havlin, H. E. Roman, Y. Goldreich, and H.-J. Schellnhuber, Phys. Rev. Lett. 81, 729 (1998). 10.1103/PhysRevLett.81.729
7. R. O. Weber and P. Talkner, J. Geophys. Res., [Atmos.] 106, 20131 (2001). 10.1029/2001JD000548
8. J. W. Kantelhardt, E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Havlin, J. Geophys. Res., [Atmos.] 111, D01106 (2006). 10.1029/2005JD005881
9. J. F. Eichner, E. Koscielny-Bunde, A. Bunde, S. Havlin, and H.-J. Schellnhuber, Phys. Rev. E 68, 046133 (2003). 10.1103/PhysRevE.68.046133
10. D. Rybski and A. Bunde, Physica A 388, 1687 (2009). 10.1016/j.physa.2008. 12.026
11. C.-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. 70, 1343 (1993). 10.1103/PhysRevLett.70.1343
12. P. C. Ivanov, A. Bunde, L. A. N. Amaral, S. Havlin, J. Fritsch-Yelle, R. M. Baevsky, H. E. Stanley, and A. L. Goldberger, Europhys. Lett. 48, 594 (1999). 10.1209/epl/i1999-00525-0
13. A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J.-H. Peter, and K. Voigt, Phys. Rev. Lett. 85, 3736 (2000). 10.1103/PhysRevLett.85.3736
14. T. Lux, Appl. Econ. Lett. 3, 701 (1996). 10.1080/135048596355691
15. Z. Ding, C. W. J. Granger, and R. F. Engle, J. Empirical Finance 1, 83 (1993). 10.1016/0927-5398(93)90006-D
16. S. Lennartz, V. N. Livina, A. Bunde, and S. Havlin, EPL 81, 69001 (2008). 10.1209/0295-5075/81/69001
17. V. N. Livina, S. Havlin, and A. Bunde, Phys. Rev. Lett. 95, 208501 (2005). 10.1103/PhysRevLett.95.208501
18. A. Bunde, J. F. Eichner, J. W. Kantelhardt, and S. Havlin, Phys. Rev. Lett. 94, 048701 (2005). 10.1103/PhysRevLett.94.048701
19. J. W. Kantelhardt, E. Koscielny-Bunde, H. H. A. Rego, S. Havlin, and A. Bunde, Physica A 295, 441 (2001). 10.1016/S0378-4371(01)00144-3
20. K. Hu, P. Ch. Ivanov, Z. Chen, P. Carpena, and H. E. Stanley, Phys. Rev. E 64, 011114 (2001). 10.1103/PhysRevE.64.011114
21. J. F. Eichner, J. W. Kantelhardt, A. Bunde, and S. Havlin, Phys. Rev. E 75, 011128 (2007). 10.1103/PhysRevE.75.011128
22. A. Arneodo, B. Audit, N. Decoster, J.-F. Muzy, and C. Vaillant, in The Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes, edited by, A. Bunde, J. Kropp, and, H.-J. Schellnhuber, (Springer, Berlin, 2002), p. 27.
23. In this technique, one first generates uncorrelated Gaussian data gi, i=1,...,N and determines its Fourier transform g k = (1/N) l=1 N gl e-2πikl/N with N/2