Identification of High-Dimensional ARMA Models with Binary-Valued Observations

Xin Li; Ting Wang; Jin Guo; Yanlong Zhao

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arXiv · 2404.01613

Identification of High-Dimensional ARMA Models with Binary-Valued Observations

Xin Li·Ting Wang·Jin Guo·Yanlong Zhao

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Abstract

This paper studies system identification of high-dimensional ARMA models with binary-valued observations. The existing paper can only deal with the case where the regression term is only one-dimensional. In this paper, the ARMA model with arbitrary dimensions is considered, which is more challenging. Different from the identification of FIR models with binary-valued observations, the prediction of original system output and the parameter both need to be estimated in ARMA models. An online identification algorithm consisting of parameter estimation and prediction of original system output is proposed. The parameter estimation and the prediction of original output are strongly coupled but mutually reinforcing. By analyzing the two estimates at the same time instead of analyzing separately, we finally prove that the parameter estimate can converge to the true parameter with convergence rate O(1/k) under certain conditions. Simulations are given to demonstrate the theoretical results.

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BibTeX RIS

Xin Li, Ting Wang, Jin Guo, Yanlong Zhao. 2024-10-28. Identification of High-Dimensional ARMA Models with Binary-Valued Observations. https://arxiv.org/abs/2404.01613

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