Abstract
This article aims to introduce the concept of substationarity for spatial point processes (SPPs). Substationarity is a new concept that has never been studied in the literature. Substationarity means that the distribution of an SPP can only be invariant under location shifts within a linear subspace of the domain. This notion lies theoretically between stationarity and nonstationarity. To formally propose the approach, the article provides the definition of substationarity and estimation of the first-order intensity function, including the subspace. As this may be unknown, we recommend using a parametric method to estimate the linear subspace and a nonparametric one to estimate the first-order intensity function given the linear subspace. It is thus a semiparametric approach. The simulation study shows that both the estimators of the linear subspace and the first-order intensity function are reliable. In an application to a Canadian 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 Canadian forest wildfire studies.
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