Modeling a nonlinear process using the exponential autoregressive time series model

Abstract

The parameter estimation methods for the nonlinear exponential autoregressive (ExpAR) model are investigated in this work. Combining the hierarchical identification principle with the negative gradient search, we derive a hierarchical stochastic gradient algorithm. Inspired by the multi-innovation identification theory, we develop a hierarchical-based multi-innovation identification algorithm for the ExpAR model. Introducing two forgetting factors, a variant of the hierarchical-based multi-innovation identification algorithm is proposed. Moreover, to compare and demonstrate the serviceability of these algorithms, a nonlinear ExpAR process is taken as an example in the simulation.

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Acknowledgements

This work was supported by the 111 Project (B12018), the National Natural Science Foundation of China (No. 61273194) and the National First-Class Discipline Program of Light Industry Technology and Engineering (LITE2018-26).

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Correspondence to Feng Ding.

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Xu, H., Ding, F. & Yang, E. Modeling a nonlinear process using the exponential autoregressive time series model. Nonlinear Dyn 95, 2079–2092 (2019). https://doi.org/10.1007/s11071-018-4677-0

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Keywords

  • Nonlinear ExpAR model
  • Parameter estimation
  • Hierarchical identification
  • Multi-innovation identification
  • Negative gradient search