Moran's I statistic-based nonparametric test with spatio-temporal observations

Moran's I statistic [Moran, (1950), ‘Notes on Continuous Stochastic Phenomena’, Biometrika, 37, 17–23] has been widely used to evaluate spatial autocorrelation. This paper is concerned with Moran's I-induced testing procedure in residual analysis. We begin with exploring the Moran's I statistic in both its original and extended forms analytically and numerically. We demonstrate that the magnitude of the statistic in general depends not only on the underlying correlation but also on certain heterogeneity in the individual observations. One should exercise caution when interpreting the outcome on correlation by the Moran's I-induced procedure. On the other hand, the effect on the Moran's I due to heterogeneity in the observations enables a regression model checking procedure with the residuals. This novel application of Moran's I is justified by simulation and illustrated by an analysis of wildfire records from Alberta, Canada.