  This paper studies system identification of high-dimensional ARMA models with
binary-valued observations. Compared with existing quantized identification of
ARMA models, this problem is more challenging since the accessible information
is much less. 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. We propose an online
identification algorithm consisting of parameter estimation and prediction of
original system output. 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.
