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Improved tests for non-linearity using network-based statistics and surrogate data

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Abstract

We report the results of studies of improved tests for non-linearity based on time series-induced network statistics and surrogate data. We compare results from the network-based statistics with the earlier tests available in the literature and demonstrate the superiority of these tests over the previous tests for several systems. The method we propose is based on constructing a network from a time series and using easily computable parameters of the resulting network such as the average path length, graph density and clustering coefficient as test statistics for the surrogate data test. These statistics are tested for their ability to distinguish between nonlinear processes and linear noise processes, using surrogate data tests on time series obtained from the Rössler system, the Lorenz system, the Henon map, the logistic map and an actual experimental time series of wind speed data, and compared with popularly used time series associated statistics. The network-based statistics are found to distinguish between the nonlinear time series and surrogates derived from the data to a higher degree than the commonly used time series-based statistics, even in the presence of measurement noise and dynamical noise. These statistics may thus prove to be of value in distinguishing between time series derived from nonlinear processes and time series obtained from linearly correlated stochastic processes even in the presence of measurement noise and dynamical noise. The results also show that the efficiency of the network parameters is not exacerbated by the presence of outliers in the given time series.

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Acknowledgements

The authors wish to thank the National Renewable Energy Laboratory (http://www.nrel.gov), USA, for making their data available and the campus computing facility of the University of Kerala under the DST-PURSE programme for providing computational facilities. They are also grateful to Dr Drisya Alex Thumba for computational assistance. The first author (MCM) would like to acknowledge the financial assistance through the e-grants scheme of the Government of Kerala.

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Authors and Affiliations

  1. Department of Futures Studies, University of Kerala, Kariavattom, 695 581, India

    M C Mallika & K Satheesh Kumar

  2. Department of Mathematics, College of Engineering, Trivandrum, 695 016, India

    K Asokan

  3. University of Kerala, Palayam, Thiruvananthapuram,   695 034, Kerala, India

    K S Anil Kumar

  4. Department of Chemical Engineering, M.S. Ramaiah Institute of Technology, MSR Nagar, Bengaluru,  560 054, India

    T R Ramamohan

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  1. M C Mallika
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  2. K Asokan
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  3. K S Anil Kumar
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  4. T R Ramamohan
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  5. K Satheesh Kumar
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Correspondence to K Satheesh Kumar.

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Mallika, M.C., Asokan, K., Kumar, K.S.A. et al. Improved tests for non-linearity using network-based statistics and surrogate data. Pramana - J Phys 95, 141 (2021). https://doi.org/10.1007/s12043-021-02181-2

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  • DOI: https://doi.org/10.1007/s12043-021-02181-2

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