  Spatial association and heterogeneity are two critical areas in the research
about spatial analysis, geography, statistics and so on. Though large amounts
of outstanding methods has been proposed and studied, there are few of them
tend to study spatial association under heterogeneous environment.
Additionally, most of the traditional methods are based on distance statistic
and spatial weighted matrix. However, in some abstract spatial situations,
distance statistic can not be applied since we can not even observe the
geographical locations directly. Meanwhile, under these circumstances, due to
invisibility of spatial positions, designing of weight matrix can not
absolutely avoid subjectivity. In this paper, a new entropy-based method, which
is data-driven and distribution-free, has been proposed to help us investigate
spatial association while fully taking the fact that heterogeneity widely
exist. Specifically, this method is not bounded with distance statistic or
weight matrix. Asymmetrical dependence is adopted to reflect the heterogeneity
in spatial association for each individual and the whole discussion in this
paper is performed on spatio-temporal data with only assuming stationary
m-dependent over time.
