Evaluation Procedures for Forecasting with Spatio-Temporal Data

The amount of available spatio-temporal data has been increasing as large-scale data collection (e.g., from geosensor networks) becomes more prevalent. This has led to an increase in spatio-temporal forecasting applications using geo-referenced time series data motivated by important domains such as environmental monitoring (e.g., air pollution index, forest fire risk prediction). Being able to properly assess the performance of new forecasting approaches is fundamental to achieve progress. However, the dependence between observations that the spatio-temporal context implies, besides being challenging in the modelling step, also raises issues for performance estimation as indicated by previous work. In this paper, we empirically compare several variants of cross-validation (CV) and out-of-sample (OOS) performance estimation procedures that respect data ordering, using both artificially generated and real-world spatio-temporal data sets. Our results show both CV and OOS reporting useful estimates. Further, they suggest that blocking may be useful in addressing CV's bias to underestimate error. OOS can be very sensitive to test size, as expected, but estimates can be improved by careful management of the temporal dimension in training.