Alternative robust estimators for autoregressive models with outliers using differential evolution algorithm

Abstract

The Least Squares (LS), Least Median Squares (LMdS), Reweighted Least Squares (RLS) and Trimmed Least Squares (TLS) estimators are used to obtain parameter estimates of AR models using DE algorithm. The empirical study indicated that, the RLS estimator seems to be very reasonable because of having smaller root mean square error (RMSE), particularly for the Gaussian AR(1) process with unknown drift and additive outliers. Moreover, while LS performs well on shorter processes with less percentage and smaller magnitude of additive outliers (AOS); RLS and TLS compare favorably with respect to LS for longer AR processes. Thus, this study recommends the Reweighted Least Squares estimator as an alternative to the LS estimator in the case of autoregressive processes with additive outliers. The experiment also demonstrates that Differential Evolution (DE) algorithm obtains optimal solutions for fitting first-order autoregressive processes with outliers using the estimators.At the request of all authors of the paper, and with the agreement of the Proceedings Editor, an updated version of this article was published on 15 December 2016. The original version supplied to AIP Publishing contained errors in some of the mathematical equations and in Table 2. The errors have been corrected in the updated and re-published article.