Time is limited on the road to asymptopia

TL;DR

This paper investigates the impact of ergodicity assumptions on the estimation of financial agent-based models, highlighting challenges in convergence and proposing strategies to improve estimation accuracy.

Contribution

It systematically explores ergodicity in FABMs, demonstrating how understanding ergodic properties of moment functions can enhance estimation methods.

Findings

Most models exhibit infeasibly long convergence times.

A strategic mix of ensemble size and simulation length improves estimation.

Understanding ergodic properties aids in addressing non-ergodic uncertainties.

Abstract

One challenge in the estimation of financial market agent-based models (FABMs) is to infer reliable insights using numerical simulations validated by only a single observed time series. Ergodicity (besides stationarity) is a strong precondition for any estimation, however it has not been systematically explored and is often simply presumed. For finite-sample lengths and limited computational resources empirical estimation always takes place in pre-asymptopia. Thus broken ergodicity must be considered the rule, but it remains largely unclear how to deal with the remaining uncertainty in non-ergodic observables. Here we show how an understanding of the ergodic properties of moment functions can help to improve the estimation of (F)ABMs. We run Monte Carlo experiments and study the convergence behaviour of moment functions of two prototype models. We find infeasibly-long convergence times for most. Choosing an efficient mix of ensemble size and simulated time length guided our estimation and might help in general.