Simulations of local Moran's index in a spatio-temporal setting.

Much research has been conducted over the last half century in developing stochastic processes, and their dynamical nature. Typically, for time indexed processes, the temporal distribution is restricted to those having marginal distributions of a specified and familiar lifetime family. Extensions of temporal models to the spatio-temporal setting can be challenging. We generalize the results from a spatial statistic that captures local correlation, Moran's index, to the spatio-temporal frame and describe a model that can be applied to temporal dynamical phenomena. The proposed approach leads to novel statistical inference results. Ensuring a foundational Moran measure is critical in describing event occurrence and progression over time of the process from observed initial conditions. In this paper, we provide a descriptive form of discrete spatio-temporal Moran's index statistics based on processes motivated by the spread of an infectious plant disease in an agricultural setting. This family possesses an underlying Poisson point process in space and time. Estimators are developed and applied to simulated data and the output are analyzed. Our results adds substantially to known results in the literature and elude to the description of the time dependent Moran's values. [ABSTRACT FROM AUTHOR]