Computer Algebra Derivation of the Bias of Burg Estimators

A symbolic method is discussed which can be used to obtain the asymptotic bias and variance to order $O(1/n)$ for estimators in stationary time series. Using this method the bias to $O(1/n)$ of the Burg estimator in AR(1) and AR(2) models is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for this bias because this problem is too intractable without using computer algebra.