A new class of high-order Yule-Walker estimates

High-order Yule-Walker equations are a, theoretically, correct tool for the computation of the AR parameters of an ARMA process. Unfortunatelly, in practical applications, working with sample data, one frequently obtain unreliable results. The high variance (in contrast with the small bias) exhibited by the corresponding AR parameter estimates is the main reason of having such a performance. Here, we propose a class of high-order Yule-Walker estimates that allow variance control in an easy form. The proposed methods, although simple to apply, are the result of a rather elaborated analysis, which also gives, as intermediate results, new insights into the practical problems of the high-order Yule-Walker equations. Although we have concentrated on ARMA processes of the AR plus white noise type, the results could be probably extended to more general cases.