Next: About this document Up: Surrogate time series Previous: Annealed surrogates

## References

1
  A. S. Weigend and N. A. Gershenfeld, eds., ``Time Series Prediction: Forecasting the future and understanding the past'', Santa Fe Institute Studies in the Science of Complexity, Proc. Vol. XV, Addison-Wesley, Reading, MA (1993).

2
  E. Ott, T. Sauer, and J. A. Yorke, ``Coping with Chaos'', Wiley, New York (1994).

3
  H. D. I. Abarbanel, ``Analysis of Observed Chaotic Data'', Springer-Verlag, Berlin, Heidelberg, New York (1996).

4
  H. Kantz and T. Schreiber, ``Nonlinear Time Series Analysis''. Cambridge University Press, Cambridge (1997).

5
  T. Schreiber, Interdisciplinary application of nonlinear time series methods, Phys. Reports 308, 1 (1998).

6
  J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, Testing for nonlinearity in time series: The method of surrogate data, Physica D 58, 77 (1992); Reprinted in [2].

7
  J. Theiler, P. S. Linsay, and D. M. Rubin, Detecting nonlinearity in data with long coherence times, in [1].

8
  J. Theiler and D. Prichard, Using `Surrogate Surrogate Data' to calibrate the actual rate of false positives in tests for nonlinearity in time series, Fields Inst. Comm. 11, 99 (1997).

9
  R. Hegger, H. Kantz, and T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package, CHAOS 9, 413 (1999). The software package is publicly available at `http://www.mpipks-dresden.mpg.de/tisean`.

10
  T. Subba Rao and M. M. Gabr, ``An introduction to bispectral analysis and bilinear time series models'', Lecture notes in statistics Vol. 24, Springer-Verlag, Berlin, Heidelberg, New York (1984).

11
  C. Diks, J. C. van Houwelingen, F. Takens, and J. DeGoede, Reversibility as a criterion for discriminating time series, Phys. Lett. A 201, 221 (1995).

12
  J. Timmer, C. Gantert, G. Deuschl, and J. Honerkamp, Characteristics of hand tremor time series, Biol. Cybern. 70, 75 (1993).

13
  T. Schreiber and A. Schmitz, Discrimination power of measures for nonlinearity in a time series, Phys. Rev. E 55, 5443 (1997).

14
  M. Palus, Testing for nonlinearity using redundancies: Quantitative and qualitative aspects, Physica D 80, 186 (1995).

15
  B. Pompe, Measuring statistical dependencies in a time series, J. Stat. Phys. 73, 587 (1993).

16
  D. Prichard and J. Theiler, Generalized redundancies for time series analysis, Physica D 84, 476 (1995).

17
  B.-L. Hao, ``Elementary Symbolic Dynamics'', World Scientific, Singapore (1989).

18
  M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A 45 3403 (1992); Reprinted in [2].

19
  D. Pierson and F. Moss, Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology, Phys. Rev. Lett. 75, 2124 (1995).

20
  P. So, E. Ott, S. J. Schiff, D. T. Kaplan, T. Sauer, and C. Grebogi, Detecting unstable periodic orbits in chaotic experimental data, Phys. Rev. Lett. 76, 4705 (1996).

21
  M. Barahona and C.-S. Poon, Detection of nonlinear dynamics in short, noisy time series, Nature 381, 215 (1996).

22
  J. E. Skinner, M. Molnar, and C. Tomberg, The point correlation dimension: Performance with nonstationary surrogate data and noise, Integrative Physiological and Behavioral Science 29, 217 (1994).

23
  M. S. Roulston, Significance testing on information theoretic functionals, Physica D 110, 62 (1997).

24
  K. Dolan, A. Witt, M. L. Spano, A. Neiman, and F. Moss, Surrogates for finding unstable periodic orbits in noisy data sets, Phys. Rev. E 59, 5235 (1999).

25
  J. Theiler and D. Prichard, Constrained-realization Monte-Carlo method for hypothesis testing, Physica D 94, 221 (1996).

26
  T. Schreiber, Constrained randomization of time series data, Phys. Rev. Lett. 80, 2105 (1998).

27
  W. A. Brock, W. D. Dechert, J. A. Scheinkman, and B. LeBaron, ``A test for independence based on the correlation dimension'', University of Wisconsin Press, Madison (1988).

28
  J. Theiler and S. Eubank, Don't bleach chaotic data, CHAOS 3, 771 (1993).

29
  B. Efron, ``The jackknife, the bootstrap and other resampling plans'', SIAM, Philadelphia, PA (1982).

30
  T. Schreiber and A. Schmitz, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett. 77, 635 (1996).

31
  D. R. Rigney, A. L. Goldberger, W. Ocasio, Y. Ichimaru, G. B. Moody, and R. Mark, Multi-channel physiological data: Description and analysis, in [1].

32
  N. E. Graham, J. Michaelsen, and T. P. Barnett, An investigation of the El Nino-Southern Oscillation cycle with statistical models - 1. Predictor field characteristics, J. Geophys. Res. 92, 1425 (1987); N. E. Graham, J. Michaelsen, and T. P. Barnett, An investigation of the El Nino-Southern Oscillation cycle with statistical models - 2. Model results, J. Geophys. Res. 92, 1427 (1987).

33
  C. L. Ehlers, J. Havstad, D. Prichard, and J. Theiler, Low doses of ethanol reduce evidence for nonlinear structure in brain activity, J. Neuroscience 18, 7474 (1998).

34
  D. Prichard and J. Theiler, Generating surrogate data for time series with several simultaneously measured variables, Phys. Rev. Lett. 73, 951 (1994).

35
  T. Bäck, ``Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms'' Oxford Univ. Press (1996).

36
  N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, Equations of state calculations by fast computing machine, J. Chem. Phys. 21, 1097 (1953).

37
  S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, Optimization by Simulated Annealing, Science 220, 671 (1983).

38
  R. V. V. Vidal, ed., ``Applied simulated annealing'', Lecture notes in economics and mathematical systems Vol. 396, Springer-Verlag, Berlin, Heidelberg, New York (1993).

39
  D. Kugiumtzis, Test Your Surrogate Data before You Test for Nonlinearity, Physical Review E, in press (1999)

40
  T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31, 207 (1986).

41
  E. Parzen, editor, ``Time Series Analysis of Irregularly Observed Data'', Lecture Notes in Statistics Vol. 25, Springer-Verlag, Berlin, Heidelberg, New York, (1983).

42
  W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, ``Numerical Recipes'', second edition, Cambridge University Press (1995).

43
  T. Schreiber and A. Schmitz, Testing for nonlinearity in unevenly sampled time series, Phys. Rev. E 59, 4044 (1999).

44
  P. M. Grootes and M. Stuiver, Oxygen 18/16 variability in Greenland snow and ice with to -year time resolution, J. Geophys. Res. 102, 26455 (1997).

45
  The Greenland Summit Ice Cores CD-ROM (1997). Available from the National Snow and Ice Data Center, University of Colorado at Boulder, and the World Data Center-A for Paleoclimatology, National Geophysical Data Center, Boulder, Colorado.

46
  E. J. Steig, P. M. Grootes, and M. Stuiver, Seasonal precipitaion timing and ice core records Science 266 1885 (1994).

47
  G. W. Frank, T. Lookman, M.A.H. Nerenberg, C. Essex, J. Lemieux, and W. Blume, Chaotic time series analyses of epileptic seizures, Physica D 46, 427 (1990).

48
  J. Theiler, On the evidence for low-dimensional chaos in an epileptic electroencephalogram, Phys. Lett. A 196, 335 (1995).

49
  J. L. Hernández, P. Valdes, and P. Vila, EEG spike and wave modelled by a stochastic limit cycle, NeuroReport 7, 2246 (1996).

50
  D. Prichard, The correlation dimension of differenced data, Phys. Lett. A 191, 245 (1994).

51
  R. W. DeBoer, J. M. Karemaker, and J. Strackee, Comparing spectra of a series of point events particularly for heart-rate-variability data IEEE Trans. Bio-Med. Eng. 31, 384 (1984).

52
  A. Schmitz and T. Schreiber, Surrogate data for non-stationary signals, Wuppertal preprint WUB-99-9 (1999).

53
  J. Timmer, The power of surrogate data testing with respect to non-stationarity, Phys. Rev. E 58, 5153 (1998).

Next: About this document Up: Surrogate time series Previous: Annealed surrogates