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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. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  2. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  3. 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.
  4. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
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  6. Rothman, P. & van Dijk, D.J.C. & Franses, Ph.H.B.F., 1999. "A multivariate STAR analysis of the relationship between money and output," Econometric Institute Research Papers EI 9945-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Christoffersen & Diebold, . "Optimal Prediction Under Asymmetric Loss," Home Pages 167, 1996., University of Pennsylvania.
  8. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
  9. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February.
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  12. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
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  18. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
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  22. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  23. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  24. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  25. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
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