Robust Estimation of Autocorrelation Parameters in the AR(1) x AR(1) Model

• Activity Number: 286
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Eric Grau*+ and J. Lu
• Affiliation(s): RTI International and Georgia Institute of Technology
• Keywords: AR(1) x AR(1) ; robust estimation ; spatial autocorrelation ; additive outlier ; Generalized Least Squares

Abstract

In this paper, we study the stationary AR(1) x AR(1) process, and present robust alternatives to the classical estimators of the autocorrelation parameters in the model. We evaluate these estimators under outlier contaminated AR(1) x AR(1) models, using an extension of the time series additive outlier (AO) model to two dimensions. We show that they perform well under these outlier models, while sacrificing a minimal amount of efficiency when outliers are not present. The usefulness of their application to real data is illustrated with three data sets from the literature. We also shall evaluate the effectiveness of these robust estimators when a mean function needs to be estimated. Using Monte Carlo simulations, we first show that, when the mean function is removed by median polish, the robust estimators of the autocorrelation parameters have smaller bias and variance than least squares or maximum likelihood estimators. Then we show how the robust estimators could be incorporated in Generalized Least Squares, and determine that a small improvement in efficiency can even be obtained in the estimation of the mean function parameters under certain outlier contaminated models.