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Analysis of the Emergent Properties: Stationarity and Ergodicity

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.

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Article provided by Journal of Artificial Societies and Social Simulation in its journal Journal of Artificial Societies and Social Simulation.

Volume (Year): 15 (2012)
Issue (Month): 2 ()
Pages: 7

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Handle: RePEc:jas:jasssj:2010-93-3
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  1. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  2. Leombruni, Roberto & Richiardi, Matteo, 2005. "Why are economists sceptical about agent-based simulations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 103-109.
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  4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  5. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  6. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  7. Gilli, M. & Winker, P., 2003. "A global optimization heuristic for estimating agent based models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 299-312, March.
  8. Domowitz, Ian & El-Gamal, Mahmoud A., 1993. "A Consistent Test of Stationary Ergodicity," Working Papers 794, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Domowitz, Ian & El-Gamal, Mahmoud A., 2001. "A consistent nonparametric test of ergodicity for time series with applications," Journal of Econometrics, Elsevier, vol. 102(2), pages 365-398, June.
  10. Matteo Richiardi & Roberto Leombruni & Nicole J. Saam & Michele Sonnessa, 2006. "A Common Protocol for Agent-Based Social Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(1), pages 15.
  11. Steven Gjerstad & Jason M. Shachat, 2007. "Individual Rationality and Market Efficiency," Purdue University Economics Working Papers 1204, Purdue University, Department of Economics.
  12. Marco LiCalzi & Paolo Pellizzari, 2008. "Zero-Intelligence Trading without Resampling," Working Papers 164, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  13. Grazzini Jakob, 2011. "Estimating Micromotives from Macrobehavior," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201111, University of Turin.
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