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Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables

Author

Listed:
  • Dean Prichard
  • James Theiler

Abstract

We propose an extension to multivariate time series of the phase-randomized Fourier-transform algorithm for generating surrogate data. Such surrogate data sets must mimic not only the autoncorrelations of each of the variables in the original data set, they must minic the cross-correlations between all the variables as well. The method is applied both to a simulated example (the three componets of the Lorenz equations) and to data from a multichannel electronencephalogram. PACS numbers: 05.45+b, 02.50.SK, 02.70.Lq, 87.80.+s

Suggested Citation

  • Dean Prichard & James Theiler, 1994. "Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables," Working Papers 94-04-023, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:94-04-023
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    Cited by:

    1. Manish Saggar & James M. Shine & Raphaël Liégeois & Nico U. F. Dosenbach & Damien Fair, 2022. "Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest," Nature Communications, Nature, vol. 13(1), pages 1-19, December.
    2. Hinich Melvin J & Mendes Eduardo M & Stone Lewi, 2005. "Detecting Nonlinearity in Time Series: Surrogate and Bootstrap Approaches," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-15, December.
    3. Andrea Beltratti & Claudio Morana, 2006. "Net Inflows and Time-Varying Alphas: The Case of Hedge Funds," ICER Working Papers 30-2006, ICER - International Centre for Economic Research.
    4. Wang, Fang & Wang, Lin & Chen, Yuming, 2022. "Multi-affine visible height correlation analysis for revealing rich structures of fractal time series," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Fredrik Charpentier Ljungqvist & Peter Thejll & Bo Christiansen & Andrea Seim & Claudia Hartl & Jan Esper, 2022. "The significance of climate variability on early modern European grain prices," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 16(1), pages 29-77, January.
    6. Hernández-Torres, David & Turpin, Christophe & Roboam, Xavier & Sareni, Bruno, 2019. "Techno-economical optimization of wind power production including lithium and/or hydrogen sizing in the context of the day ahead market in island grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 158(C), pages 162-178.
    7. Dashtian, Hassan & Jafari, G. Reza & Sahimi, Muhammad & Masihi, Mohsen, 2011. "Scaling, multifractality, and long-range correlations in well log data of large-scale porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2096-2111.
    8. Milan Palus & L. Pecen & D. Pivka, 1995. "Estimating Predictability: Redundancy and Surrogate Data Method," Working Papers 95-07-060, Santa Fe Institute.
    9. Przyborski, Marek, 2002. "Possible determinism and the real world data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 297-303.
    10. Gao, Wei & Zhao, Hongxia, 2013. "Conditional independence graph for nonlinear time series and its application to international financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2460-2469.
    11. Chong Hong & Beom Kim, 2011. "Mutual information and redundancy for categorical data," Statistical Papers, Springer, vol. 52(1), pages 17-31, February.
    12. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.

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