On robust estimation in the first order autoregressive processes

Abstract

Estimation of the parameter φ of an autoregressive process of order one, {Xt}, is considered. An estimaticn procedure referred to as the Median Substitute (MS) method based on the empirical median of {Xt−1Xt} is proposed. φMS, the MS estimate of φ, is proven to be consistent and asymptotically normal. A simulation study is carried out to show the viability of the proposed method in comparison with some other robust procedures.