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

TL;DR

This paper develops an online identification algorithm for high-dimensional ARMA models with binary observations, enabling simultaneous parameter estimation and output prediction, with proven convergence properties.

Contribution

It extends ARMA system identification to high-dimensional cases with binary data, introducing a coupled estimation method with convergence guarantees.

Findings

Parameter estimates converge to true values at rate O(1/k)

The proposed algorithm effectively predicts system output

Simulations validate theoretical convergence results

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.