System Identification Based Instability Detection of Noisy ARMA Systems

We investigate the ability of system identification estimation methods to detect the instability of an ARMA system with measurement noise. We consider a range of cases of stable and unstable systems together with estimators based on least squares and on Yule-Walker equations of varying orders, with an aim to understanding the capacity of the methods to detect the instability of the underlying system from a finite data set. Our analysis uses asymptotic and non-asymptotic results, but is focused on the question of correctly estimating the unstable parts of the system.