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A consistent test for nonlinear out of sample predictive accuracy

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  • Corradi, Valentina
  • Swanson, Norman R.

Abstract

In this paper, we draw on both the consistent specification testing and the predictive ability testing literatures and propose a test for predictive accuracy which is consistent against generic nonlinear alternatives. Broadly speaking, given a particular reference model, assume that the objective is to test whether there exists any alternative model, among an infinite number of alternatives, that has better predictive accuracy than the reference model, for a given loss function. A typical example is the case in which the reference model is a simple autoregressive model and the objective is to check whether a more accurate forecasting model can be constructed by including possibly unknown (non)linear functions of the past of the process or of the past of some other process(es). We propose a statistic which is similar in spirit to that of White (2000), although our approach differs from his as we allow for an infinite number of competing models that may be nested. In addition, we allow for non vanishing parameter estimation error. In order to construct valid asymptotic critical values, we implement a conditional p-value procedure which extends the work of Inoue (1999) by allowing for non vanishing parameter estimation error.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 110 (2002)
Issue (Month): 2 (October)
Pages: 353-381

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Handle: RePEc:eee:econom:v:110:y:2002:i:2:p:353-381

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
  2. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
  3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
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  5. 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.
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  7. Todd E. Clark & Michael McCracken, 1999. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Computing in Economics and Finance 1999 1241, Society for Computational Economics.
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  9. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
  10. Christoffersen, Peter F & Diebold, Francis X, 1996. "Further Results on Forecasting and Model Selection under Asymmetric Loss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 561-71, Sept.-Oct.
  11. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  12. repec:att:wimass:9710 is not listed on IDEAS
  13. Phillip Rothman & Dick van Dijk & Philip Hans Franses, 2000. "A Multivariate STAR Analysis of the Relationship Between Money and Output," Working Papers 0012, East Carolina University, Department of Economics.
  14. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
  15. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
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  23. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February.
  24. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  25. Swanson, Norman R & White, Halbert, 1995. "A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 265-75, July.
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