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An investigation of tests for linearity and the accuracy of likelihood based inference using random fields

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  • Christian M. Dahl

Abstract

We analyze the random field regression model approach recently suggested by Hamilton (2001, Econometrica, 69, 537--73). We show through extensive simulation studies that although the random field approach is indeed very closely related to the non-parametric spline smoother it seems to offer several advantages over the latter. First, tests for neglected nonlinearity based on Hamilton's random field approach seem to be more powerful than existing test statistics developed within the context of the multivariate spline smoother approach. Second, the convergence properties of the random field approach in limited samples appear to be significantly better than those of the multivariate spline smoother. Finally, when compared to the popular neural network approach the random field approach also performs very well. These results provide strong support for the view of Harvey and Koopman (2000, Econometrics Journal, 3, 84--107) that model-based kernels or splines have a sounder statistical justification than those typically used in non-parametric work. Copyright Royal Economic Society, 2002

Suggested Citation

  • Christian M. Dahl, 2002. "An investigation of tests for linearity and the accuracy of likelihood based inference using random fields," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 263-284, June.
  • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:2:p:263-284
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    Cited by:

    1. Pablo Gonzalez & Mauricio Tejada, 2006. "No linealidades en la regla de política monetaria del Banco Central de Chile: una evidencia empírica," Revista de Analisis Economico – Economic Analysis Review, Ilades-Georgetown University, Universidad Alberto Hurtado/School of Economics and Bussines, vol. 21(1), pages 81-115, July.
    2. Dong Heon Kim, 2004. "Nonlinearity in the Term Structure," Econometric Society 2004 Far Eastern Meetings 440, Econometric Society.
    3. Denise R. Osborn & Dong Heon Kim & Marianne Sensier, 2005. "Nonlinearity in the Fed's monetary policy rule," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 621-639.
    4. Dahl, Christian M. & Gonzalez-Rivera, Gloria, 2003. "Testing for neglected nonlinearity in regression models based on the theory of random fields," Journal of Econometrics, Elsevier, vol. 114(1), pages 141-164, May.
    5. Derek Bond & Michael J. Harrison & Niall Hession & Edward J. O'Brien, 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Trinity Economics Papers tep2006, Trinity College Dublin, Department of Economics.
    6. Huang, Ho-Chuan, 2005. "Diverging evidence of convergence hypothesis," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 233-255, June.
    7. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    8. Chihwa Kao & Yongmiao Hong, 2004. "Detecting Neglected Nonlinearity in Dynamic Panel Data with Time-Varying Conditional Heteroskedasticity," Econometric Society 2004 Far Eastern Meetings 753, Econometric Society.
    9. repec:wyi:journl:002062 is not listed on IDEAS
    10. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2007. "Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity," The Economic and Social Review, Economic and Social Studies, vol. 38(1), pages 1-24.
    11. D H Kim, 2005. "Nonlinearity in the Term Structure," Centre for Growth and Business Cycle Research Discussion Paper Series 51, Economics, The Univeristy of Manchester.
    12. Hamilton, James D., 2003. "What is an oil shock?," Journal of Econometrics, Elsevier, vol. 113(2), pages 363-398, April.
    13. He, Jie & Richard, Patrick, 2010. "Environmental Kuznets curve for CO2 in Canada," Ecological Economics, Elsevier, vol. 69(5), pages 1083-1093, March.
    14. D H Kim, 2004. "Nonlinearity in the Term Structure," The School of Economics Discussion Paper Series 0401, Economics, The University of Manchester.
    15. Tae-Hwy Lee & Zhou Xi & Ru Zhang, 2013. "Testing for Neglected Nonlinearity Using Regularized Artificial Neural Networks," Working Papers 201422, University of California at Riverside, Department of Economics, revised Apr 2012.
    16. Dahl, Christian M. & Hylleberg, Svend, 2004. "Flexible regression models and relative forecast performance," International Journal of Forecasting, Elsevier, vol. 20(2), pages 201-217.
    17. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics.

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