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A Comparison of Nonlinear Stochastic Self-Exciting Threshold Autoregressive and Chaotic k-Nearest Neighbour Models in Daily Streamflow Forecasting

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Abstract

A nonlinear stochastic self-exciting threshold autoregressive (SETAR) model and a chaotic k-nearest neighbour (k-nn) model, for the first time, were compared in one and multi-step ahead daily flow forecasting for nine rivers with low, medium, and high flows in the western United States. The embedding dimension and the number of nearest neighbours of the k-nn model and the parameters of the SETAR model were identified by a trial-and-error process and a least mean square error estimation method, respectively. Employing the recursive forecasting strategy for the first time in multi-step forecasting of SETAR and k-nn, the results indicated that SETAR is superior to k-nn by means of performance indices. SETAR models were found to be more efficient in forecasting flows in one and multi-step forecasting. SETAR is less sensitive to the propagated error variances than the k-nn model, particularly for larger lead times (i.e., 5 days). The k-nn model should carefully be used in multi-step ahead forecasting where peak flow forecasting is important by considering the risk of error propagation.

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Acknowledgments

The authors would like to thank the U.S. Geological Survey for providing data used in this study.

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Authors and Affiliations

  1. Engineering Faculty, Department of Civil Engineering, Süleyman Demirel University, Isparta, Turkey

    Hakan Tongal

  2. Faculty of Engineering Technology, Department of Water Engineering and Management, University of Twente, Enschede, The Netherlands

    Martijn J. Booij

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  1. Hakan Tongal
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  2. Martijn J. Booij
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Correspondence to Hakan Tongal.

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Tongal, H., Booij, M.J. A Comparison of Nonlinear Stochastic Self-Exciting Threshold Autoregressive and Chaotic k-Nearest Neighbour Models in Daily Streamflow Forecasting. Water Resour Manage 30, 1515–1531 (2016). https://doi.org/10.1007/s11269-016-1237-6

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  • DOI: https://doi.org/10.1007/s11269-016-1237-6

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