Simulating multivariate time series using flocking

Notions from agent based modeling (ABM) can be used to simulate multivariate time series. An example is given using the ABM concept of flocking, which models the behaviors of birds (called boids) in a flock. A multivariate time series is mapped into the coordinates of a bounded orthotope. This represents the flight path of a boid. Other boids are generated that flock around this data boid. The coordinates of these new boids are mapped back to simulate replicates of the original time series. The flock size determines the number of replicates. The similarity of the replicates to the original time series can be controlled by flocking parameters to reflect the strength of the belief that the future will mimic the past. It is potentially possible to replicate general non-stationary, dependent, high-dimensional time series in this manner.