Analysis of the Emergent Properties: Stationarity and Ergodicity

Abstract

This paper illustrates the use of the nonparametric Wald-Wolfowitz test to detect stationarity and ergodicity in agent-based models. A nonparametric test is needed due to the practical impossibility to understand how the random component influences the emergent properties of the model in many agent-based models. Nonparametric tests on real data often lack power and this problem is addressed by applying the Wald-Wolfowitz test to the simulated data. The performance of the tests is evaluated using Monte Carlo simulations of a stochastic process with known properties. It is shown that with appropriate settings the tests can detect non-stationarity and non-ergodicity. Knowing whether a model is ergodic and stationary is essential in order to understand its behavior and the real system it is intended to represent; quantitative analysis of the artificial data helps to acquire such knowledge.

Macroeconomic Policy in DSGE and Agent-Based Models Redux: New Developments and Challenges Ahead

“…Recent research indeed provide alternatives to the researcher interested in statistically assessing such an issue, and therefore better understand the behavior of the model, and draw inferences about the real system it is intended to represent (Richiardi et al, 2006). As an example, Grazzini (2012) discusses the use of Wald-Wolfowitz tests applied to ABMs and shows that, under appropriate settings, these procedures can detect non-stationarity and non-ergodicity.…”

Megtakarítási típusok - egy adaptív-evolúciós megközelítés

“…mi egy olyan módszert választottunk, amelyet többször alkalmaztak ágensalapú modellekre, és amely a Wald-Wolfowitz-teszt (Wald-Wolfowitz [1940]) kiterjesztése (Grazzini [2012]). …”

“…a szimbólumokra a futamtesztet kétoldali alternatív hipotézissel alkalmaztuk (lásd Grazzini [2012]). amennyiben a részminták átlagai véletlenszerűen szóródnak a teljes átlag körül, a stacionaritás nullhipotézisét az első momentum esetén nem tudjuk elutasítani.…”

Agent-Based Model Calibration Using Machine Learning Surrogates

“…Such properties emerge indeed from the repeated interactions among ecologies of heterogeneous, boundedly-rational and adaptive agents. 1 As a result, the dynamic properties of the system cannot be studied analytically, the identification of causal mechanisms is not always possible and interactions give rise to the emergence of relationships that cannot simply be deduced by aggregating those of micro variables (Anderson et al, 1972, Tesfatsion and Judd, 2006, Grazzini, 2012, Gallegati and Kirman, 2012. This raises the issue of finding appropriate tools to investigate the emergent behavior of the model with respect to different parameter settings, random seeds, and initial conditions (see also Lee et al, 2015).…”