Testing for Spatial Autocorrelation: The Regressors that Make the Power Disappear

Abstract

We show that for any sample size, any size of the test, and any weights matrix outside a small class of exceptions, there exists a positive measure set of regression spaces such that the power of the Cliff-Ord test vanishes as the autocorrelation increases in a spatial error model. This result extends to the tests that define the Gaussian power envelope of all invariant tests for residual spatial autocorrelation. In most cases, the regression spaces such that the problem occurs depend on the size of the test, but there also exist regression spaces such that the power vanishes regardless of the size. A characterization of such particularly hostile regression spaces is provided.

How to avoid the zero-power trap in testing for correlation

“…The former proposition proves (and generalizes) an observation already made in the discussion section of Krämer (1985). The latter proposition is obtained by generalizing an argument in Martellosio (2012), who considered the same question in a spatial autoregressive setting. Essentially, these two propositions show (for the tests based on the specific family of test statistics and the corresponding critical values considered) respectively that (i) the zero-power trap arises for generic design matrices (i.e., up to a Lebesgue null set of exceptional matrices) for small enough critical values; and (ii) for any critical value that leads to a size in (0, 1) there exists an open set of design matrices for which the zero-power trap arises.…”

Point optimal testing: A survey of the post 1987 literature

“…Since 1987, point optimal invariant tests have been proposed for a wide range of testing problems involving the covariance matrix in the linear regression model. These include (i) testing for autocorrelation in the presence of missing observations (Shively, 1993), (ii) testing for first order autoregressive (AR 1)disturbances when the data is made up of the aggregate of a large number of small samples (Bhatti, 1992), (iii) testing for spatial autocorrelation in the disturbances (Martellosio, 2010(Martellosio, , 2012, (iv) testing for block effects caused by random coefficients (Bhatti and Barry, 1995), (v) testing for quarter-dependent simple fourth-order autoregressive (AR(4)) disturbances (Wu and King, 1996), (vi) testing for joint AR(1)-AR(4) disturbances against joint MA(1)-MA 4disturbances (Silvapulle and King, 1993) and (vii) testing for the presence of a particular error component (El- Bassiouni and Charif, 2004). Hwang and Schmidt (1996) extended the work of Dufour and King (1991) Dufour and King's (1991) tests, the main difference being the treatment of the initial observation.…”

Consistent Misspecification Testing in Spatial Autoregressive Models

“…These tests have employed common approaches such as Wald, Lagrange Multiplier or Likelihood Ratio methods in the spatial setting. Among many others, see Burridge (1980), Cliff and Ord (1981), Kelejian and Prucha (2001), Anselin (2001), Robinson (2008), Lee and Yu (2012), Martellosio (2012) and Delgado and Robinson (2015).…”