  The goal of the article is to develop the approach of substationarity to
spatial point processes (SPPs). Substationarity is a new concept, which has
never been studied in the literature. It means that the distribution of SPPs
can only be invariant under location shifts within a linear subspace of the
domain. Theoretically, substationarity is a concept between stationariy and
nonstationarity, but it belongs to nonstationarity. To formally propose the
approach, the article provides the definition of substationarity and an
estimation method for the first-order intensity function. As the linear
subspace may be unknown, it recommends using a parametric way to estimate the
linear subspace and a nonparametric way to estimate the first-order intensity
function, indicating that it is a semiparametric approach. The simulation
studies show that both the estimators of the linear subspace and the
first-order intensity function are reliable. In an application to a forest
wildfire data set, the article concludes that substationarity of wildfire
occurrences may be assumed along the longitude, indicating that latitude is a
more important factor than longitude in forest wildfire studies.
