A non-subjective approach to the GP algorithm for analysing noisy time series

Physica D: Nonlinear Phenomena

Volumn 215, Issue 2, 2006, Pages 137-145

  Harikrishnan, K P ^a   Misra, R ^b   Ambika, G ^c   Kembhavi, A K ^b  

^a The Cochin College   (India)

^b INTER UNIVERSITY CENTRE FOR ASTRONOMY AND ASTROPHYSICS   (India)

^c MAHARAJA S COLLEGE   (India)

Author keywords

Chaos; Correlation dimension; Surrogate analysis

Indexed keywords

ALGORITHMS; ASTROPHYSICS; BRAIN; CHAOS THEORY; CORRELATION METHODS; DATA REDUCTION; ELECTROENCEPHALOGRAPHY; WHITE NOISE;

CORRELATION DIMENSION; GRASSBERGER-PROCCACIA (GP) ALGORITHM; NOISY TIME SERIES; SURROGATE ANALYSIS;

TIME SERIES ANALYSIS;

EID: 33748101898     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.01.027     Document Type: Article

References (39)

1. Grassberger P., and Proccacia I. Measuring the strangeness of strange attractors. Physica D 9 (1983) 189
2. Grassberger P., and Proccacia I. Characterisation of strange attractors. Phys. Rev. Lett. 50 (1983) 346
3. Schreiber T. Inter disciplinary applications of time series analysis. Phys. Rep. 308 (1999) 1
4. Aberbanel H.D.L. Analysis of Observed Chaotic Data (1996), Springer, New York
5. Sprott J.C. Chaos and Time Series Analysis (2003), Oxford Univ. Press, New York
6. Serre T., Kollath Z., and Buchler J.R. Search for low dimensional nonlinear behavior in irregular variable stars. Astronomy Astrophys. 311 (1996) 833
7. Raidl A. Estimating the fractal dimension, K2 entropy and predictability of the atmosphere. Czechoslovak. J. Phys. 46 (1996) 293
8. Ramsey J.B., and Yuen H. Bias and error bars in dimension calculations and their evaluation in some simple models. Phys. Lett. A 134 (1988) 287
9. Eckmann J.P., Jarvenpaa E., Jarvenpaa M., and Proccacia I. Estimating the Correlation Dimension of the Visible Universe (2003). http://astro-ph/0301034
10. Silva C., Pimentel I.R., Andrada A., Fored J.P., and Soares E.D. Correlation dimension maps of EEG from epileptic absences. Brain Topography 11 (1999) 201
11. Ding M., Grebogi C., Ott E., Sauer T., and Yorke J.A. Plateau onset for correlation dimension: When does it occur?. Phys. Rev. Lett. 70 (1993) 3872
12. Smith L.A. Intrinsic limits on dimension calculations. Phys. Lett. A 133 (1988) 283
13. Dvorak I., and Klashka J. Modification of the Grassberger-Proccacia algorithm for estimating correlation exponent of chaotic systems with high embedding dimension. Phys. Lett. A 145 (1990) 225
14. Casdagli M., Eubank S., Farmer J.D., and Gibson J. State space reconstruction in the presence of noise. Physica D 51 (1991) 52
15. Schreiber T. Determination of noise level of chaotic time series. Phys. Rev. E 48 (1993) R13
16. Diks C. Estimating invariants of noisy attractors. Phys. Rev. E 53 (1996) 4263
17. Osborne A.R., and Provenzale A. Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35 (1989) 357
18. I± ) noise. Phys. Lett. A 155 (1991) 480
19. Redaelli S., Plewczynski D., and Macek W.M. Influence of colored noise on chaotic systems. Phys. Rev. E 66 (2002) 035202 (R)
20. Theiler J., Eubank S., Longtin A., Galdrikian B., and Farmer J.D. Testing for nonlinearity in time series: the method of surrogate data. Physica D 58 (1992) 77
21. Schreiber T., and Schmitz A. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77 (1996) 635
22. Kantz H., and Schreiber T. Nonlinear Time Series Analysis (1997), Cambridge University Press, Cambridge
23. Kennel M.B., and Isabelle S. Method to distinguish possible chaos from colored noise and to determine embedding parameters. Phys. Rev. A 46 (1992) 3111
24. Judd K. An improved estimator of dimension and some comments on providing confidence intervals. Physica D 56 (1992) 216
25. Small M., and Judd K. Detecting nonlinearity in experimental data. Internat. J. Bifur. Chaos 8 (1998) 1231
26. Judd K. Estimating dimension from small samples. Physica D 71 (1994) 421
27. Sprott J.C., and Rowlands G. Improved correlation dimension calculation. Internat. J. Bifur. Chaos 11 (2001) 1865
28. Grassberger P. Finite sample corrections to entropy and dimension estimates. Phys. Lett. A 128 (1988) 369
29. Ramsey J.B., Sayers C.L., and Rothman P. The statistical properties of dimension calculations using small data sets-economic applications. Internat. Econom. Rev. 31 (1990) 991
30. Yu D., Small M., Harrison R.G., and Diks C. Efficient implementation of Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data. Phys. Rev. E 61 (2000) 3750
31. Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points. Phys. Rev. A 36 (1987) 4456
32. Nolte G., Ziehe A., and Muller K.R. Noise robust estimates of correlation and K2 entropy. Phys. Rev. E 64 (2001) 016112 (1-10)
33. Sander T., Wubbeler G., Lueschow A., Curio G., and Trahms L. Nonlinear time series analysis for human alpha rhythm. IEEE Trans. Biomed. Eng. 49 (2002) 345
34. Guerrero A., and Smith L.A. Towards coherent estimation of correlation dimension. Phys. Lett. A 318 (2003) 373
35. Kugiumtzis D. Test your surrogate data before you test for nonlinearity. Phys. Rev. E 60 (1999) 2808
36. Hegger R., Kantz H., and Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9 (1999) 413
37. Schreiber T., and Schmitz A. Surrogate time series. Physica D 142 (2000) 346
38. Misra R., Harikrishnan K.P., Mukhopadhyay B., Ambika G., and Kembhavi A.K. Chaotic behavior of the black hole system GRS1915 + 105. Astrophys. J. 609 (2004) 313
39. Andrzejak R.G., Lehnertz K., Mormann F., Rieke C., David P., and Elger C.E. Indications of nonlinear deterministic and finite dimensional structures in time series of brain electrical activity. Phys. Rev. E 64 (2001) 061907