On Sequential Least Squares Estimates of Autoregressive Parameters

For estimation of the parameters of a stable autoregressive process AR( p ) by the least squares method, the paper proposes to use a particular stopping rule that essentially depends on the behavior of the minimal eigenvalue of the observed Fisher information matrix. The upper bounds for the mean square error of estimation are derived in the cases of known and unknown variances of the noise. Asymptotic formulas for the mean of the stopping time are given in both cases.