Testing for nonlinearity in time series: The method of surrogate data

Conference · Tue Jan 01 00:00:00 EST 1991

OSTI ID:6026813

Theiler, J; Galdrikian, B; Longtin, A ^[1]; Eubank, S; Farmer, J D ^[2]

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1. Los Alamos National Lab., NM (United States)
2. Los Alamos National Lab., NM (United States) Santa Fe Inst., NM (United States)

We describe a statistical approach for identifying nonlinearity in time series; in particular, we want to avoid claims of chaos when simpler models (such as linearly correlated noise) can explain the data. The method requires a careful statement of the null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. We present algorithms for generating surrogate data under various null hypotheses, and we show the results of numerical experiments on artificial data using correlation dimension, Lyapunov exponent, and forecasting error as discriminating statistics. Finally, we consider a number of experimental time series -- including sunspots, electroencephalogram (EEG) signals, and fluid convection -- and evaluate the statistical significance of the evidence for nonlinear structure in each case. 56 refs., 8 figs.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE; DOHHS; USDOE, Washington, DC (United States); Department of Health and Human Services, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6026813
• Report Number(s): LA-UR-91-3343; CONF-9108181-1; ON: DE92002463; CNN: 1-R01-MH47184-01
• Resource Relation: Conference: Symposium on interpretation of time series from mechanical systems, Warwick (United Kingdom), 25-30 Aug 1991
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
TIME-SERIES ANALYSIS
NONLINEAR PROBLEMS
ALGORITHMS
CONVECTION
NOISE
RANDOMNESS
STATISTICS
SUNSPOTS
TESTING
ENERGY TRANSFER
HEAT TRANSFER
MASS TRANSFER
MATHEMATICAL LOGIC
MATHEMATICS
SOLAR ACTIVITY
STARSPOTS
STELLAR ACTIVITY
990200* - Mathematics & Computers