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

Abstract

Spurious regression occurs when two independent stationary or nonstationary time series are found to be correlated. Spurious behaviour is also detected in spatial data. Using a Monte Carlo analysis, this study examines the spurious phenomenon for two independent stationary spatial autoregressive processes of order one, that is, SAR(1), and it finds that when spatial econometric models are estimated, as suggested by the LM specification tests, the spurious behaviour is not detected nor the presence of spatially autocorrelated errors.

Keywords:

• spurious regression
• stationary spatial autoregressive SAR(1) processes
• LM dependence tests
• spatial autocorrelated errors

JEL Classification:

• C20
• C21
• C22

Notes

¹ The whole simulation process is conducted by R using the SPDEP package developed by Bivand (2015).

² Table 1 presents simulations results using rook and queen contiguity definitions without torus correction. The simulation process is also implemented with torus correction and the empirical results are not reported as they are very similar with those obtained without torus correction. The only difference is that for small sample sizes and for given values of the autoregressive parameter the null hypothesis is rejected at a smaller rate.

³ The mean values of Moran’s I test statistic for model specifications (2) and (3), not shown in Table 2, are all close to zero.