Tukey smoothers as preprocessors for positive ar(1) parameter estimation in the presence of additive contamination

Abstract

An ordinary least squares estimator of a parameter φ has minimum mean squared error among all unbiased linear estimators of φ but can be drastically affected by outliers in the data. A robust approach, based on using Tukey smoothers as data preprocessors, is proposed for estimating positive parameters φ of AR(1) time series. For series with additive contamination, the proposed procedure, suitably applied, is shown to achieve substantially smaller mean squared error in estimating φ than does ordinary least squares estimation.

Keywords:

• Tukey smoothers
• AR(1) process
• outliers
• additive contamination
• robust estimation