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Modeling a nonlinear process using the exponential autoregressive time series model

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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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