Performance comparison of autoregressive estimation methods

The statistical performances of six methods in the finite sample estimation of the autoregressive (AR) parameters and the spectral peak frequencies are comparatively studied. The methods are: the Yule Walker method, Burg´s method, the Box Jenkins least square method, the forward error method, the forward backward error method, and Kay´s RMLE method. Precise performance statistics are obtained analytically for the AR(1) parameter estimators. For higher order processes similar evaluation is not feasible; computer simulation results are presented. The relative performances of the methods in the processing of stationary AR time series are found to be dependent on the characteristic root positions of the underlying AR processes. Methods that are superior are identified.