A Frequency Domain Test for a Spatial Unit Root Process

Stationarity is a common assumption in statistical inference when data come from a random field, but this hypothesis has to be checked. In this paper, we build a frequency domain statistical test to check a unit root for a spatial autoregressive model, and find its asymptotic distribution. Later, we use Monte Carlo simulations to obtain the small sample properties of the proposed statistical test, and we find that the size of the test is good, and the power of the test improves if the spatial autocorrelation coefficient decreases. Additionally, we find that the size of our test is better than other spatial unit root tests when the data generating process is not a spatial autoregressive model. Finally, we propose a methodology to use frequency domain tests in regional data, and we use it to do an application. Specifically, we study data of electricity demand in the Department of Antioquia (Colombia), and find that statistical evidence based on different tests suggests that electricity consumption does not have a spatial unit root; as a consequence, parameter estimates are sensible. Specifically, we find that the price elasticity of electricity demand is -1.150 while the income elasticity is 0.408