The Effects of Spatial Aggregation on Spatial Time Series Modeling and Forecasting

Abstract

Spatio-temporal data analysis involves modeling a variable observed at different locations over time. A key component of space-time modeling is determining the spatial scale of the data. This dissertation addresses the following three questions: 1) How does spatial aggregation impact the properties of the variable and its model? 2) What spatial scale of the data produces more accurate forecasts of the aggregate variable? 3) What properties lead to the smallest information loss due to spatial aggregation? Answers to these questions involve a thorough examination of two common space-time models: the STARMA and GSTARMA models. These results are helpful to researchers seeking to understand the impact of spatial aggregation on temporal and spatial correlation as well as to modelers interested in determining a spatial scale for the data. Two data examples are included to illustrate the findings, and they concern states' annual labor force totals and monthly burglary counts for police districts in the city of Philadelphia.