Non-nested testing of spatial correlation

Abstract

a b s t r a c tWe develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all dimensions; both isotropic models and nonisotropic models can be considered, and a wide variety of correlation structures. In the second case, models involving spatial weight matrices are covered, such as ''spatial autoregressive models''. The setting is sufficiently general to potentially cover other parametric structures such as certain factor models, and vector-valued observations, and here our preliminary asymptotic theory for parameter estimates is of some independent value. The test statistic is based on a Gaussian pseudo-likelihood ratio, and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct; this limit theory rests strongly on a central limit theorem for the Gaussian pseudo-maximum likelihood parameter estimates. A small Monte Carlo study of finite-sample performance is included.

Estimation of Spatial Autoregressions With Stochastic Weight Matrices

“…Therefore it is an identification condition which can be compared to those already in the literature. The closest conditions may be found in Gupta and Robinson (2018) and Delgado and Robinson (2015), the latter showing the equivalence of their condition to that of Lee (2004) in the case of SAR models. With deterministic weight matrices, the latter interprets the condition as related to the uniqueness of the covariance matrix of y.…”

“…Assumption 14 also holds with Ξ(τ ) − Ξ τ † replaced by Ξ(τ ) −1 − Ξ τ † −1 due to Assumption 13, and is useful in an equicontinuity argument in the consistency proof. Further discussion of it may be found in Delgado and Robinson (2015), who also discuss sufficient conditions for it to hold. Write…”

“…Both papers take independent disturbances that are also identically distributed in the case of Lee (2004) but need not be in Gupta and Robinson (2018). On the other hand, Delgado and Robinson (2015) provide asymptotic theory for estimation of spatial models of a rather general type, including SAR, spatial moving average (SMA) and spatial ARMA, allowing a linear process type disturbance structure for their distributional results.…”

“…An additional innovation is that we allow for a general 'spatial linear process' structure in the disturbances, cf. Robinson and Thawornkaiwong (2012) and Delgado and Robinson (2015). The former do not consider models with spatial lags in the dependent variables explicitly, nor do they provide theory for OLS or PMLE, while the latter do not consider models with regressors.…”

Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension

“…Assumption 7 is an identification condition related to the uniqueness of the covariance matrix of y n , introduced in Delgado and Robinson (2014) who discuss it and compare it to the identification condition employed by Lee (2004) in his asymptotic theory.…”