Further evidence on alternative procedures for testing of spatial autocorrelation among regression disturbances

Abstract

It is well-known that the least-squares estimator of the vector of coefficients in a linear regression model is not Best-Linear Unbiased in the presence of autocorrelation. The problem was first recognized by statisticians dealing with temporal regression analysis. This led to the development of tests for temporal autocorrelation (see, for example, von Neumann, 1941; Durbin and Watson, 1950, 1951 and 1971). Because these tests require estimators for the unknown disturbances, attention was paid to the development of procedures to estimate the vector of disturbances. Apart from the obvious ordinary least squares (OLS) residuals we mention the best-linear unbiased scalar covariance (BLUS) estimator, which was proposed by Theil (1965) and Koerts (1967), and the best-linear unbiased fixed co- variance (BLUF) residuals, which are described in Dubbelman, Abrahamse and Koerts (1972). Recently, Phillips and Harvey (1974) proposed a recursive procedure to obtain estimates of the errors. Because their estimator also has the LUS properties, we will refer to it as the RELUS-vector.

The authors are indebted to Cornelis P. A. Bartels for providing his experiences in the field and for suggesting improvements on the paper.