Instability detection of ARMA systems based on AR system identification

The ability of parametric autoregressive (AR) system identification methods to detect the instability of an autoregressive moving average (ARMA) system of an unknown order is investigated. The collection of least squares AR estimators of various orders is shown to have the capacity to detect the instability of the underlying system. Necessary information is not the order of the system but, instead, an upper bound of the number of unstable poles with the maximal magnitude outside the unit circle.