On the robust estimation of the autocorrelation coefficients of stationary sequences

This paper discusses methods for the estimation of the autocorrelation coefficients of a finite-dependent stationary random sequence. Three estimators are examined: the sample average and two proposed approaches, namely the pseudo-maximum-likelihood (pseudo-ML) estimator and the pseudo-M estimator. The latter scheme is found as a solution of a Fredholm integral equation. All three estimators are first studied for specific distribution models. Then the existence of a minimax robust design is proved and a suboptimally robust scheme is proposed. Simulation results illustrate the theoretical foundations of the methods and indicate that the pseudo-M estimator achieves significantly better performance than the other two schemes when tested against dependent data and in the presence of outliers. Finally, the results may also be applied to the estimation of a location parameter of a dependent random sequence.