Nonlinear Dynamics

, Volume 95, Issue 3, pp 2079–2092 | Cite as

Modeling a nonlinear process using the exponential autoregressive time series model

  • Huan Xu
  • Feng DingEmail author
  • Erfu Yang
Original Paper


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.


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



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).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Internet of Things EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  2. 2.College of Automation and Electronic EngineeringQingdao University of Science and TechnologyQingdaoPeople’s Republic of China
  3. 3.Space Mechatronic Systems Technology LaboratoryUniversity of StrathclydeGlasgowUnited Kingdom

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