Efficient on-line estimation of autoregressive parameters

New procedures for estimating autoregressive parameters in AR(m) models are proposed. The proposed method allows for incorporation of auxiliary information into the estimation process and produces estimation procedures, which are consistent and asymptotically efficient under certain regularity conditions. Also, these procedures are naturally on-line and do not require storing all the data. Theoretical results are presented in the case when m = 1. Two important particular cases are considered in detail: linear procedures and likelihood procedures with the LS truncations. A specific example is also presented to briefly discuss some practical aspects of applications of the procedures of this type. © 2010 Allerton Press, Inc.