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

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 de...

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Bibliographic Details
Published in:	IET control theory & applications Vol. 14; no. 2; pp. 262 - 270
Main Authors:	Xu, Huan, Ding, Feng, Yang, Erfu
Format:	Journal Article
Language:	English
Published:	The Institution of Engineering and Technology 29.01.2020
Subjects:	appropriate innovation length autoregressive moving average processes average noise coloured noise ExpARMA model exponential autoregressive time series model extended stochastic gradient algorithm forgetting factor gradient methods gradient search least squares approximations MI‐ESG algorithm multiinnovation ESG algorithm multiinnovation identification theory nonlinear exponential autoregressive model optimal step‐size parameter estimation parameter estimation accuracy recursive estimation recursive parameter estimation problems recursive search‐based identification algorithms Research Article stochastic processes time series unknown parameters least squares approximations appropriate innovation length autoregressive moving average processes parameter estimation accuracy average noise time series recursive search-based identification algorithms recursive parameter estimation problems optimal step-size multiinnovation identification theory multiinnovation ESG algorithm nonlinear exponential autoregressive model MI-ESG algorithm gradient search recursive estimation forgetting factor coloured noise parameter estimation extended stochastic gradient algorithm stochastic processes gradient methods unknown parameters exponential autoregressive time series model ExpARMA model
ISSN:	1751-8644, 1751-8652
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Summary:	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.
ISSN:	1751-8644 1751-8652
DOI:	10.1049/iet-cta.2019.0429