SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series

Chaos, Solitons and Fractals

Volumn 37, Issue 1, 2008, Pages 187-202

  Vitanov, Nikolay K ^a   Sakai, Kenshi ^b   Dimitrova, Zlatinka I ^c  

^a INSTITUTE OF MECHANICS   (Bulgaria)

^b TOKYO UNIVERSITY OF AGRICULTURE AND TECHNOLOGY   (Japan)

^c INSTITUTE OF SOLID STATE PHYSICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

AGRICULTURAL ENGINEERING; AUTOCORRELATION; PHASE SPACE METHODS; PRINCIPAL COMPONENT ANALYSIS; SPECTRUM ANALYSIS; TIME DELAY; TIME SERIES ANALYSIS;

AUTOCORRELATION FUNCTION ANALYSIS (ACFA); NONSTATIONARY TIME SERIES; SINGULAR SPECTRUM ANALYSIS (SSA); TIME DELAY PHASE SPACE CONSTRUCTION (TDPSC);

INFORMATION DISSEMINATION;

EID: 39149141586     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.08.043     Document Type: Article

References (61)

1. Vautard R., and Ghil M. Singular spectrum analysis in nonlinear dynamics with application to paleoclimatic time series. Physica D 35 (1989) 395-424
2. Vautard R., Yiou P., and Ghil M. Singular spectrum analysis - a tookit for short noisy chaotic signals. Physica D 58 (1992) 95-126
3. Sharma A.S., Vassiliadis D., and Papadoupoulos K. Reconstruction of low-dimensional magnetospheric dynamics by singular spectrum analysis. Geophys Res Lett 20 (1993) 335-338
4. Schlesinger M.E., and Ramankutty. An oscillation in the global climate system of period 65-75 years. Nature 367 (1994) 723-726
5. Robertson AW. Interdecadal variability over the North Pacific in a multi-century climate. Clim Dyn 12:227-241.
6. Moron V., Vautard R., and Ghil M. Trends, interdecadal and interannual oscillations in global sea surface. Clim Dyn 14 (1998) 545-569
7. Kravtsov S., and Ghil M. Interdecadal variability in a hybrid coupled ocean-atmosphere-sea ice model. J Phys Oceanogr 34 (2004) 1756-1775
8. Kondrashov D., Feliks Y., and Ghil M. Oscillatory modes on extended Nile River records (AD622-1922). Geophys Res Lett 32 (2005) Art. No. L10702
9. Dima M., and Lohmann C. Fundamental and derived modes of climate variability: concept and application to interannual time-scales. TELLUS 56A (2004) 229-249
10. Baratta D., Cicioni G., Masulli F., and Studer L. Application of an ensemble technique based on singular spectrum analysis to daily rainfall forecast. Neural Networks 16 (2003) 375-387
11. Alonso F.J., Del Castillo J.M., and Pintado P. Application of singular spectrum analysis to the smoothing of raw kinematic signals. J Biomech 38 (2005) 1085-1092
12. Marelli L., Bilato R., Franz P., Martin P., Murari A., and O'Gorman M. Singular spectrum analysis as a tool for plasma fluctuations analysis. Rev Scientific Instrum 72 (2001) 499-502
13. Theobald C.M., Glassey C.A., Horgan G.W., and Robinson C.D. Principal component analysis of landmarks from reversible images. J Roy Statist Soc C - Appl Statist 53 (2004) 163-175
14. Wold S., Esbensen K., and Geladi P. Principal component analysis. Chemometrics Intell Lab Syst 2 (1987) 37-52
15. Carland J.L., and Mills A.L. Classification and characterization of heterothropic microbial communities on the basis of patterns of community-level sole-carbon-source utilization. Appl Environ Microbiol 57 (1991) 2351-2359
16. Tatusov R.L., Natale D.A., Garkavtsev I.V., Tatusova T.A., Shankavaram U.T., Rao B.S., et al. The COG database: new developments in phylogenetic classification of proteins from complete genomes. Nucleic Acids Res 29 (2001) 22-28
17. Daffertshoffer A., Lamot C.J.C., Mejer O.G., and Beek P.J. PCA in studying coordination and variability: a tutorial. Clin Biomech 19 (2004) 415-428
18. Russell E.L., Chiang L.H., and Braatz R.D. Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis. Chemometric Intell Lab Syst 51 (2000) 81-93
19. Sakai K. Nonlinear dynamics and chaos in agricultural systems (2001), Elsevier, London
20. Vitanov N.K., and Sakai K. Upper bounds on the number of significant degrees of freedom of noise-influenced oscillations of moving machines. Syst Anal Model Simul (SAMS) 43 (2003) 815-828
21. Vitanov N.K., Sakai K., and Yankulova E.D. On correlations and fractal characteristics of time series. J Theoret Appl Mech 35 N2 (2005) 73-90
22. Schultz T.W. Agriculture in an unstable economy (1945), McGraw-Hill, New York
23. Cochrane W.W. Farm prices: myth and reality (1958), University of Minessota Press, Minneapolis
24. Gill G.I. Seasonality and agriculture in the developing world: A problem of the poor and powerless (1991), Cambridge University Press, Cambridge
25. In: O'Callaghan J.R. (Ed). Land use. The interaction of economics, ecology and hydrology (1996), Chapman & Hall, London
26. Seitz W.D., Nelson G., and Halcrow H. Economics of resources, agriculture and food (2001), McGraw-Hill, Irvin
27. In: Just R.E., and Pope R.D. (Eds). A comprehensive assessment of the role of risk in US agriculture (2002), Kluwer, Norwell
28. Kantz H., and Schreiber T. Nonlinear time series analysis (1997), Cambridge University Press, Cambridge
29. Böck T., and Vitanov N.K. Low dimensional chaos in zero-Prandtl-number Benard Marangoni convection. Phys Rev E 65 (2002) Art. No. 037203
30. Kantz H., Holstein D., Ragwitz M., and Vitanov N.K. Markov chain model for turbulent wind speed data. Physica A 342 (2004) 315-321
31. Dimitrova Z.I., and Vitanov N.K. Chaotic pairwise competition. Theoret Populat Biol 66 (2004) 1-12
32. Vitanov N.K., Dimitrova Z.I., and Kantz H. On the trap of extinction and its elimination. Phys Lett A 349 (2006) 350-355
33. Chavas J.P., and Holt M.T. Market instability and nonlinear dynamics. Am J Agricult Econom 75 (1993) 113-120
34. Lorenz E.N. Deterministic nonperiodic flow. J Atmos Sci 20 (1963) 130-141
35. Pyragas V., and Pyragas A. Delayed feedback control of the Lorenz system: An analytical treatment at a subcritical Hopf bifurcation. Phys Rev E 73 (2006) Art. No. 036215
36. Misra A.A., and Sanghi S.A. study of the assymetric Malkus waterwheel: The biased Lorenz equations. CHAOS 16 (2006) Art. No. 013114
37. Cannon A.J. Nonlinear principal predictor analysis: Application to the Lorenz system. J Clim 19 (2006) 579-589
38. Chen Z.M., and Price W.G. On the relation between Rayleigh-Benard convection and Lorenz system. Chaos Solitons & Fractals 28 (2006) 571-578
39. Cuomo K.M., and Oppenheim A.V. Circuit implementation of synchronized chaos with applications to communications. Phys Rev Lett 71 (1993) 65-68
40. Bai E.W., and Lonngren K. Synchronization of two Lorenz systems using active control. Chaos Solitons & Fractals 8 (1997) 51-58
41. Panchev S., and Vitanov N.K. Asymptotic properties of some complex Lorenz systems. J Calcutta Math Soc 1 (2005) 181-190
42. Panchev S., Spassova T., and Vitanov N.K. Analytical and numerical investigation of two Lorenz-like dynamical systems. Chaos Solitons & Fractals 33 (2007) 1658-1671
43. Hegger R., Kantz H., and Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9 (1999) 413-435
44. Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A 185 (1994) 77-87
45. Schreiber T. Interdisciplinary applications of nonlinear time series methods. Phys Rep 308 (1999) 2-64
46. Dimitrova Z.I., and Vitanov N.K. Adaptation and its impact on the dynamics of a system of three competing populations. Physica A 300 (2001) 91-115
47. Dimitrova Z.I., and Vitanov N.K. Influence of adaptation on the nonlinear dynamics of a system of competing populations. Phys Lett A 272 (2000) 368-380
48. Dimitrova Z.I., and Vitanov N.K. Dynamical consequences of adaptation of the growth rates in a system of three competing populations. J Phys A: Math General 34 (2001) 7459-7473
49. Kantelhard J.W., Koscielny-Bunde E., Rego H.H.A., Havlin S., and Bunde A. Detecting long-range correlations with detrended fluctuation analysis. Physica A 295 (2001) 441-454
50. Kantelhardt J.W., Zschiegner S.A., Koscielny-Bunde E., Havlin S., Bunde A., and Stanley H.E. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316 (2002) 87-114
51. Ivanov P.C., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Struzik Z.R., et al. Multifractality in human heartbeat dynamics. Nature 399 (1999) 461-465
52. Muzy J.F., Bacry E., and Arneodo A. The multifractal formalism revisited with wavelets. Int J Bif Chaos 4 (1994) 245-302
53. Vitanov N.K., and Yankulova E.D. Multifractal analysis of the long-range correlations of the heartbeat activity of Drosophila melanogaster. Chaos Solitons & Fractals 28 (2006) 768-775
54. Broomhead D.S., and King G.P. Extracting qualitative dynamics from experimental data. Physica D 20 (1986) 217-236
55. Albano A.M., Muench J., Schwant C., Mees A.I., and Rapp P.E. Singular-value decomposition and the Grassberger-Procaccia algorithm. Phys Rev A 38 (1988) 3017-3026
56. Mees A.I., Rapp P.E., and Jennings L.S. Singular-value decomposition and embedding dimension. Phys Rev A 36 (1987) 340-346
57. Sauer T., Yorke J.A., and Casdagli M. Embedology. J Stat Phys 65 (1991) 579-616
58. Abarbanel H.D.I., Brown R., Sidorowich J.J., and Tsirming L.S. The analysis of observed chaotic data in physical systems. Rev Mod Phys 65 (1993) 1331-1392
59. Farmer J.D., and Sidorowich J.J. Predicting chaotic time series. Phys Rev Lett 59 (1987) 845-848
60. Kantz H., and Schreiber T. Dimension estimates and physiological data. Chaos 5 (1995) 143-154
61. Hegger R., Kantz H., Matassini L., and Schreiber T. Coping with nonstationarity by overembedding. Phys Rev Lett 84 (2000) 4092-4095