Does Calibration Affect the Complexity of Agent-Based Models? A Multifractal Grid Analysis

We examine the complexity of financial returns generated by popular agent-based models through studying multifractal properties of such time series. Specifically, we are interested in the sensitivity of the models to their parameter settings and whether some patterns emerge in the connection between complexity and a specific type of parameter. We find that (i) herding behavior mostly boosts the model complexity as measured by multifractality, (ii) various in-built stabilizing factors increase model complexity, (iii) the role of intensity of choice as well as the chartists' representation have rather model-specific effects, and (iv) the number of agents has no statistically significant effect on the model complexity. The heterogeneous set of nine analyzed models thus offers some universal concepts that hold across their range. Our results also indicate that interesting dynamics are observed not only for the benchmark parameter settings but also for other combinations of parameter values for most models. This opens new avenues for future research and specifically motivates examining the models in more detail by focusing on other dynamic properties in addition to the herein presented multifractality