IDEAS home Printed from https://ideas.repec.org/a/jas/jasssj/2010-93-3.html
   My bibliography  Save this article

Analysis of the Emergent Properties: Stationarity and Ergodicity

Author

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.

Suggested Citation

  • Jakob Grazzini, 2012. "Analysis of the Emergent Properties: Stationarity and Ergodicity," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(2), pages 1-7.
    • Handle: RePEc:jas:jasssj:2010-93-3
    as

    Download full text from publisher

    File URL: https://www.jasss.org/15/2/7/7.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    2. Marco LiCalzi & Paolo Pellizzari, 2008. "Zero-Intelligence Trading Without Resampling," Lecture Notes in Economics and Mathematical Systems, in: Klaus Schredelseker & Florian Hauser (ed.), Complexity and Artificial Markets, chapter 1, pages 3-14, Springer.
    3. 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 1-15.
    4. 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.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. 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 1057-1072, June.
    7. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70(3), pages 322-322.
    8. 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.
    9. Steven Gjerstad & Jason M. Shachat, 2007. "Individual Rationality and Market Efficiency," Purdue University Economics Working Papers 1204, Purdue University, Department of Economics.
    10. Grazzini Jakob, 2011. "Estimating Micromotives from Macrobehavior," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201111, University of Turin.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    12. 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.
    13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    14. Domowitz, Ian & El-Gamal, Mahmoud A., 1993. "A Consistent Test of Stationary-Ergodicity," Econometric Theory, Cambridge University Press, vol. 9(4), pages 589-601, August.
    15. repec:bla:jecsur:v:12:y:1998:i:5:p:423-69 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jürgen Wolters & Uwe Hassler, 2006. "Unit root testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 43-58, March.
    2. Grazzini, Jakob & Richiardi, Matteo, 2015. "Estimation of ergodic agent-based models by simulated minimum distance," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 148-165.
    3. Nielsen, Morten Ørregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1515-1544, December.
    4. Morten Ø. Nielsen, 2008. "A Powerful Tuning Parameter Free Test Of The Autoregressive Unit Root Hypothesis," Working Paper 1175, Economics Department, Queen's University.
    5. Jiti Gao & Maxwell King, 2011. "A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors," Monash Econometrics and Business Statistics Working Papers 20/11, Monash University, Department of Econometrics and Business Statistics.
    6. Isabel Cortés-Jiménez & Manuel Artís, 2005. "The role of the tourism sector in economic development - Lessons from the Spanish experience," ERSA conference papers ersa05p488, European Regional Science Association.
    7. Frédérique Bec & Mélika Ben Salem & Marine Carrasco, 2010. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model," Annals of Economics and Statistics, GENES, issue 99-100, pages 395-427.
    8. Hondroyiannis, George & Lolos, Sarantis & Papapetrou, Evangelia, 2005. "Financial markets and economic growth in Greece, 1986-1999," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(2), pages 173-188, April.
    9. Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
    10. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    11. Maghyereh, A., 2004. "Oil Price Shocks and Emerging Stock Markets: A Generalized VAR Approach," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 1(2), pages 27-40.
    12. Hayashi, Naotsugu, 2005. "Structural changes and unit roots in Japan's macroeconomic time series: is real business cycle theory supported?," Japan and the World Economy, Elsevier, vol. 17(2), pages 239-259, April.
    13. Hondroyiannis, George, 2004. "Estimating residential demand for electricity in Greece," Energy Economics, Elsevier, vol. 26(3), pages 319-334, May.
    14. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    15. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    16. George Hondroyiannis & Evangelia Papapetrou, 2001. "An Investigation of the Public Deficts and Government Spending Relationship: Evidence for Greece," Public Choice, Springer, vol. 107(1), pages 169-182, April.
    17. S.P. Jayasooriya, 2009. "A Dynamic Equilibrium between Inflation and Minimum Wages in Sri Lanka," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 3(2), pages 113-132, April.
    18. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2006. "Modified tests for a change in persistence," Journal of Econometrics, Elsevier, vol. 134(2), pages 441-469, October.
    19. Baillie, R. & Chung, C. & Tieslau, M., 1992. "The Long Memory and Variability of Inflation : A Reappraisal of the Friedman Hypothesis," Other publications TiSEM 49a709f4-608f-43c5-840b-c, Tilburg University, School of Economics and Management.
    20. Hondroyiannis, George & Papapetrou, Evangelia, 2006. "Stock returns and inflation in Greece: A Markov switching approach," Review of Financial Economics, Elsevier, vol. 15(1), pages 76-94.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jas:jasssj:2010-93-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Francesco Renzini (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.