Analysis of the Emergent Properties: Stationarity and Ergodicity

Jakob Grazzini

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)N/A-N/A
Number of pages15
Publication statusPublished - 2012


  • Agent-Based
  • Ergodicity
  • Simulations
  • Stationarity
  • Statistical Test


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