Leverages and Influential Observations in a Regression Model with Autocorrelated Errors

Abstract

This article deals with the general form of the hat matrix and the DFBETA measure to detect the influential observations and the leverages in the linear regression model with more than one regressor when the errors are from AR(1) and AR(2) processes. Previous studies dealing with the influential observations and the leverages in the constant mean model and regression through the origin model are obtained as special cases. To demonstrate the utility of the hat matrix and the DFBETA measure, two numerical examples based on the ice cream consumption data with AR(1) errors and the Fox-Hartnagel data with AR(2) errors are analyzed. The results show that the parameter of the autoregressive process affects the influential and leverage points.

Keywords:

• Autocorrelated error
• Influence
• Leverages
• Generalized least squares estimator

Mathematics Subject Classification:

• Primary 62J20
• Secondary 62J07