Open AccessRecursive search‐based identification algorithms for the exponential autoregressive time series model with coloured noise
Author(s) -
Xu Huan,
Ding Feng,
Yang Erfu
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0429
Subject(s) - autoregressive model , algorithm , noise (video) , estimation theory , identification (biology) , series (stratigraphy) , exponential function , forgetting , system identification , computer science , mathematics , time series , autoregressive–moving average model , star model , autoregressive integrated moving average , mathematical optimization , artificial intelligence , machine learning , statistics , data modeling , paleontology , mathematical analysis , linguistics , botany , philosophy , database , image (mathematics) , biology
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.