Exploiting autoregressive properties to develop prospective urban arson forecasts by target

• We estimate prospective arson hotspot models for Detroit, Michigan.
• We evaluate how the aggregation of data across space affects arson forecast skill.
• We compare statistical models that differently address the autoregressivity of arson.
• Out-of-sample performance shows models cannot exploit autoregressivity at fine scales.
• Spatial data aggregation tends to increase forecast accuracy for arson in Detroit.

Municipal fire departments responded to approximately 53,000 intentionally-set fires annually from 2003 to 2007, according to National Fire Protection Association figures. A disproportionate amount of these fires occur in spatio-temporal clusters, making them predictable and, perhaps, preventable. The objective of this research is to evaluate how the aggregation of data across space and target types (residential, non-residential, vehicle, outdoor and other) affects daily arson forecast accuracy for several target types of arson, and the ability to leverage information quantifying the autoregressive nature of intentional firesetting. To do this, we estimate, for the city of Detroit, Michigan, competing statistical models that differ in their ability to recognize potential temporal autoregressivity in the daily count of arson fires. Spatial units vary from Census tracts, police precincts, to citywide. We find that (1) the out-of-sample performance of prospective hotspot models for arson cannot usefully exploit the autoregressive properties of arson at fine spatial scales, even though autoregression is significant in-sample, hinting at a possible bias-variance tradeoff; (2) aggregation of arson across reported targets can yield a model that differs from by-target models; (3) spatial aggregation of data tends to increase forecast accuracy of arson due partly to the ability to account for temporally dynamic firesetting; and (4) arson forecast models that recognize temporal autoregression can be used to forecast daily arson fire activity at the Citywide scale in Detroit. These results suggest a tradeoff between the collection of high resolution spatial data and the use of more sophisticated modeling techniques that explicitly account for temporal correlation.