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Linear versus Nonlinear Macroeconomies: A Statistical Test


  • Ashley, Richard A
  • Patterson, Douglas M


A statistical test based on the estimated bispectrum is presented, which can distinguish between the linear stochastic dynamics widely used in macroeconomic models and alternative nonlinear dynamic mechanisms, including both nonlinear stochastic models and nonlinear deterministic (chaotic) models. The test is applied to an aggregate stock market index and to an aggregate industrial production index. In both cases, the test easily rejects the null hypothesis of a linear stochastic generating mechanism. This result strongly suggests that nonlinear dynamics (deterministic or stochastic) should be an important feature of any empirically plausible macroeconomic model. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • 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.
  • Handle: RePEc:ier:iecrev:v:30:y:1989:i:3:p:685-704

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    References listed on IDEAS

    1. Shell, Karl, 1971. "Notes on the Economics of Infinity," Journal of Political Economy, University of Chicago Press, vol. 79(5), pages 1002-1011, Sept.-Oct.
    2. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
    3. Galor, Oded, 1988. "The Long-run Implications of a Hicks-Neutral Technical Progress," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 177-183, February.
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    Cited by:

    1. Aghababa, Hajar & Barnett, William A., 2016. "Dynamic structure of the spot price of crude oil: does time aggregation matter?," Energy Economics, Elsevier, vol. 59(C), pages 227-237.
    2. Teles, Paulo & Wei, William W. S., 2000. "The effects of temporal aggregation on tests of linearity of a time series," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 91-103, July.
    3. Jeyanthi Karuppiah & Cornelis A. Los, 2000. "Wavelet Multiresolution Analysis of High-Frequency FX Rates, Summer 1997," School of Economics Working Papers 2000-06, University of Adelaide, School of Economics.
    4. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    5. Peter Kugler, 1990. "Sind Wechselkursfluktuationen zufällig oder chaotisch?," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 126(II), pages 113-129, June.
    6. Stephanie Rendón de la Torre, 2012. "Estimación del coeficiente de Hurst con wavelets de índices accionarios de Turquía, Indonesia, México y Corea del Sur," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 6(2), pages 27-50.
    7. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
    8. Valderrama, Diego, 2007. "Statistical nonlinearities in the business cycle: A challenge for the canonical RBC model," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 2957-2983, September.
    9. Maurice Peat & Max Stevenson, 1995. "Testing for Nonlinearities in Economic and Financial Time Series," Working Paper Series 48, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    10. Elena Rusticelli & Richard Ashley & Estela Bee Dagum & Douglas Patterson, 2009. "A New Bispectral Test for NonLinear Serial Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 279-293.
    11. Karuppiah, Jeyanthi & Los, Cornelis A., 2005. "Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
    12. Diego Valderrama, 2002. "Nonlinearities in international business cycles," Working Paper Series 2002-23, Federal Reserve Bank of San Francisco.
    13. Diego Valderrama, 2003. "Statistical Nonlinearities in the Business Cycle," Computing in Economics and Finance 2003 219, Society for Computational Economics.
    14. T Tang, 2009. "Testing for Non-linearity in the Balancing Item of Balance of Payments Accounts: The Case of 20 Industrial Countries," Economic Issues Journal Articles, Economic Issues, vol. 14(2), pages 107-124, September.
    15. João Paulo Martin Faleiros & Denisard Cnéio de Oliveira Alves, 2006. "Não Linearidade Nos Ciclos De Negócios: Modelo Auto-Regressivo “Smooth Transition” Para O Índice Geral De Produção Industrial Brasileiro E Bens De Capital," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 10, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
    16. Lubos Briatka, 2006. "How Big is Big Enough? Justifying Results of the iid Test Based on the Correlation Integral in the Non-Normal World," CERGE-EI Working Papers wp308, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    17. Liu, Yamei, 2000. "Overfitting and forecasting: linear versus non-linear time series models," ISU General Staff Papers 2000010108000014914, Iowa State University, Department of Economics.
    18. Peter Martey Addo & Monica Billio & Dominique Guegan, 2012. "Studies in Nonlinear Dynamics and Wavelets for Business Cycle Analysis," Documents de travail du Centre d'Economie de la Sorbonne 12023r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2013.
    19. Dufrenot Gilles & Mathieu Laurent, 1994. "Methods In Economics: Testing For Linearity," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 5(2-3), pages 1-16, June.
    20. Pfann, Gerard A., 1996. "Factor demand models with nonlinear short-run fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 315-331.
    21. David Chappell & Robert Eldridge, 1997. "Non-linear characteristics of the sterling/European Currency Unit exchange rate: 1984-1992," The European Journal of Finance, Taylor & Francis Journals, vol. 3(2), pages 159-182.
    22. Vinodh Madhavan, 2014. "Investigating the nature of nonlinearity in Indian Exchange Traded Funds (ETFs)," Managerial Finance, Emerald Group Publishing, vol. 40(4), pages 395-415, March.

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