Recursive search-based identification algorithms for the exponential autoregressive time series model with coloured noise

Huan Xu, Feng Ding, Erfu Yang

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3 Citations (Scopus)
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This study focuses on the recursive parameter estimation problems for the non-linear exponential autoregressive model with moving average noise (the ExpARMA model for short). By means of the gradient search, an extended stochastic gradient (ESG) algorithm is derived. Considering the difficulty of determining the step-size in the ESG algorithm, a numerical approach is proposed to obtain the optimal step-size. In order to improve the parameter estimation accuracy, the authors employ the multi-innovation identification theory to develop a multi-innovation ESG (MI-ESG) algorithm for the ExpARMA model. Introducing a forgetting factor into the MI-ESG algorithm, the parameter estimation accuracy can be further improved. With an appropriate innovation length and forgetting factor, the variant of the MI-ESG algorithm is effective to identify all the unknown parameters of the ExpARMA model. A simulation example is provided to test the proposed algorithms.

Original languageEnglish
Pages (from-to)262-270
Number of pages9
JournalIET Control Theory and Applications
Issue number2
Early online date9 Oct 2019
Publication statusPublished - 29 Jan 2020


  • ExpARMA model
  • extended stochastic gradient algorithm
  • e recursive parameter estimation problems

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