Detecting Non-negligible New Influences in Environmental Data via a General Spatio-temporal Autoregressive Model

Abstract

In some environmental problems, it is required to find out if new influences (e.g., new influences on the ozone concentration) occurred in one area of the region (named as a treatment area) have affected the measurements there substantially. For convenience, the area of the region that is free of influences is named as the control area. To tackle such problems, we propose a change-point detection approach. We first introduce a general spatio-temporal autoregressive (GSTAR) model for the environmental data, which takes into account effects of different spatial location surroundings, seasonal cyclicities, temporal correlations among observations at the same locations and spatial correlations among observations from different locations. An EM-type algorithm is provided for estimating the parameters in a GSTAR model. We then respectively model the data collected from the treatment and control areas of the region by the GSTAR models. If new influences occurred in the treatment area are not negligible, there should be detectable changes in the time-dependent regression coefficients in the GSTAR model for that area compared to those in the GSTAR model for the control area. A change-point detection method can be applied to the differences of regression coefficient estimates of these two models. We illustrate our method through one real data example of daily ozone concentration measurements and one simulated data example with two scenarios.