A Small Sample Property of the Cliff-Ord Test for Spatial Correlation

SUMMARY The Cliff-Ord test for spatial correlation in regression disturbances is found to be a locally CLIFF and ORD (1973) proposed a test for spatial correlation in regression disturbances. They informally argued that for values of the spatial correlation parameter, p, in the neighbourhood of zero, their test coincides with the likelihood ratio test derived assuming the value of p under the alternative hypothesis is known. Recently, Burridge (1980) demonstrated that the Cliff-Ord test is identical to the Lagrange multiplier test and is therefore asymptotically equivalent to the likelihood ratio test. In this note we examine some of the test's small sample power properties. It is found to be a Locally Best Invariant (LBI) test in the neighbourhood of p = 0, while for a special type of spatial correlation and when the regression has an intercept, it is a Uniformly Most Powerful Invariant (UMPI) test. Consider the usual linear regression model,