Bounds on the accuracy of Gaussian ARMA parameter estimation methods based on sample covariances

The asymptotic accuracy of Gaussian ARMA parameter estimation methods based on a fixed number of sample covariances is considered. Several key results are briefly reviewed, including: i) a general asymptotic expression for the error covariance of the ARMA parameter estimates; ii) the fact that this error covariance is always greater than a certain lower bound; iii) the fact that this lower bound is strictly greater than the Cramer-Rao bound; iv) an explicit ARMA estimation technique that asymptotically achieves the bound. The key result of this note is a proof that this lower bound approaches the Cramer-Rao bound as the number of sample covariances tends to infinity.