Unit Roots and Deterministic Trends in Spatial Econometric Models

Abstract

This article reflects on the relevance of the concept of unit roots in the spatial context. The initial introduction of this topic in the time-series literature caused significant changes in the mainstream econometric methodology. However, the literature specialized in spatial econometric modeling has not extensively dealt with this issue. The current article continues the discussion of the concept of unit roots employed in a spatial context and presents a series of peculiarities that should be noticed. Subsequently, attention focuses on the topic of deterministic trends associated with the scale factor that intervenes in autoregressive spatial processes. The incidence of this type of trend should not be neglected. It induces the risk of finding spurious correlation that should be taken into account.

Is spurious behaviour an issue for two independent stationary spatial autoregressive SAR(1) processes?

“…E-mail: agiaklis@unipi.gr Applied Economics Letters, 2015Letters, http://dx.doi.org/10.1080Letters, /13504851.2015 autocorrelated producing large values of the Moran's I test statistic. Mur and Trivez (2003) extended Fingleton's work by including a deterministic intercept in the spatial processes and found spurious results in the concept of spatial deterministic trends, indicating also that the LM tests for spatial dependence, as presented by Anselin et al (1996), produce confusing results. Therefore, it is very interesting to examine the spurious regression phenomenon for two independent stationary spatial autoregressive processes of order one, SAR(1), using a Monte Carlo analysis, and to evaluate its performance based on the LM specification tests.…”

Testing for Unit Roots and Cointegration in Spatial Cross-Section Data

“…The spatial DGPs studied by Fingleton have zero spatial drift, hence the correct adjective is nonsense rather than spurious. By contrast the DGP in Mur and Trivez (2003) has spatial drift, so that the adjective spurious is fitting in their case.…”

“…3 Fingleton (1999) and Mur and Trivez (2003) assume that there is an unconnected spatial unit, which provides space with an artificial beginning. We drop this assumption.…”

Detecting Dependence Between Spatial Processes

“…Mur and Trivez (2003) extend this problem to series that are spatially autocorrelated, not necessarily near nonstationarity, but with a strong deterministic component. If this is the case, the bivariate Moran's I, both in the Geoda and in the Czaplewski-Reich version, will reject the null hypothesis due to the strong autocorrelation existing in the series.…”