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A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos

Author

Listed:
  • William A. Barnett

    (Washington University in St. Louis)

  • A. Ronald Gallant

    (University of North Carolina at Chapel Hill)

  • Melvin J. Hinich

    (University of Texas at Austin)

  • Jochen A. Jungeilges

    (University of Osnabruck, Germany)

  • Daniel T. Kaplan

    (Macalester College)

  • Mark J. Jensen

    (Southern Illinois University at Carbondale)

Abstract

This is the FINAL draft of this paper reporting the results of a long ongoing competition. The paper now is forthcoming in the Journal of Econometrics. This final version replaces the earlier draft that was also in this archive. Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We apply five highly regarded tests for nonlinearity or chaos to ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos. The simulated data and the code for some of the tests entered into this competition also are online in this archive.

Suggested Citation

  • William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, University Library of Munich, Germany, revised 29 Jan 1997.
  • Handle: RePEc:wpa:wuwpem:9602005
    Note: Type of Document - Microsoft Word; prepared on Macintosh; to print on PostScript; pages: 49 ; 2 figures: included. The simulated data used in this competition is online in this archive at URL location:
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    References listed on IDEAS

    as
    1. Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 301-320, July.
    2. Apostolos Serletis, 2006. "Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money," World Scientific Book Chapters, in: Money And The Economy, chapter 6, pages 119-130, World Scientific Publishing Co. Pte. Ltd..
    3. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
    4. William Barnett & Ping Chen, 2016. "Economic Theory as a Generator of Measurable Attractors," Mondes en développement, De Boeck Université, vol. 0(3), pages 171-171.
    5. DeCoster, Gregory P & Mitchell, Douglas W, 1991. "Nonlinear Monetary Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 455-461, October.
    6. Ramsey, James B & Sayers, Chera L & Rothman, Philip, 1990. "The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(4), pages 991-1020, November.
    7. DeCoster, Gregory P. & Mitchell, Douglas W., 1992. "Dynamic implications of chaotic monetary policy," Journal of Macroeconomics, Elsevier, vol. 14(2), pages 267-287.
    8. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    9. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    10. Ashley, Richard A & Patterson, Douglas M, 1989. "Linear versus Nonlinear Macroeconomies: A Statistical Test," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 685-704, August.
    11. Richard A. Ashley & Douglas M. Patterson & Melvin J. Hinich, 1986. "A Diagnostic Test For Nonlinear Serial Dependence In Time Series Fitting Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 165-178, May.
    12. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
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    More about this item

    Keywords

    chaos nonlinearity competition experiment;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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