Matrix-Based Computation of the Exact Cramer-Rao Bound for the ARMA Parameter Estimation Realized with Relatively Short Data Records

摘要

The paper presents a simple algorithm for the computation of exact Cramer-Rao bound (CRB) on unbiased estimates of the parameters of autoregressive moving-average (ARMA) processes. The proposed algorithm is based on the matrix representation of a causal ARMA process having uniformly sampled finite number of data points. The formulae derived for obtaining the exact Fisher information matrix (FIM), its inverse yields the CRB, are an explicit function of the ARMA model parameters. It is noteworthy that the proposed algorithm has a simple formulation, and is more convenient for relatively short data records.