Statistical analysis of spatially homogeneous dynamic agent-based processes using functional time series analysis

Dynamic systems consisting of multiple interacting autonomous individuals are of particular interest in a number of scientific fields, including ecology, biology, and swarm robotics. Such systems are commonly referred to as agent-based processes. Detection and characterisation of agent-agent interactions is an important step in the analysis of agent-based processes, however existing statistical methods are relatively limited. This paper presents a novel framework for investigating spatial interactions between agents combining techniques from spatial statistics and functional time series analysis. Assuming second order spatial equilibrium of the agent-based process, we develop a test for identifying the specific nature of interactions between agents. We also consider methodology for validating the assumption of spatial equilibrium for a given realisation of the agent-based process. The efficacy of this methodology is demonstrated via Monte Carlo simulation studies and an application to experimental data obtained by observing a species of flightless locust.