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Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives

  • Jonathan B. Hill

We develop LM-tests of linearity that are consistent against a class of Compound Smooth Transition Autoregressive (CoSTAR) models of the conditional mean. Our method is an extension of the sup-test developed by Bierens (1990) and Bierens and Plobeger (1997), provides maximal power against popular STAR alternatives and is consistent against any deviation from the null hypothesis. Moreover, the test method can be extended to consistent tests of number of threshold regimes, flexible parametric forms, conditional homoscedasticity against linear or smooth transition GARCH, and causality tests of out-of-sample predictive accuracy. Of particular note, we improve on Bierens's (1990) test theory by considering vector conditional moments which lead to an LM sup-test statistic that is never degenerate under the alternative of functional mis-specification. Moreover, our test is a true test against smooth transition alternatives, whereas the universally employed polynomial regression test of Teräsvirta (1994) requires the assumption that the true data generating mechanism is STAR. A simulation study demonstrates that the suggested STAR sup-statistic renders a test with superlative empirical size and power attributes, in particular in comparison to the Bierens (1990) test, the neural test by Lee, White and Granger (1993), and specifically the polynomial regression test employed throughout the STAR literature. Finally, we apply the new tests to various macroeconomic processes

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 42.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:42
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  1. Oscar Jorda & Alvaro Escribano, 2003. "Improved Testing And Specification Of Smooth Transition Regression Models," Working Papers 9726, University of California, Davis, Department of Economics.
  2. Skalin, Joakim, 1998. "Testing linearity against smooth transition autoregression using a parametric bootstrap," SSE/EFI Working Paper Series in Economics and Finance 276, Stockholm School of Economics, revised 13 Dec 1998.
  3. Friedman, Benjamin M & Kuttner, Kenneth N, 1992. "Money, Income, Prices, and Interest Rates," American Economic Review, American Economic Association, vol. 82(3), pages 472-92, June.
  4. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
  5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, june. pag.
  6. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  7. Dijk, Dick van & Franses, Philip Hans, 1999. "Modeling Multiple Regimes in the Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 3(03), pages 311-340, September.
  8. Stock, James H. & Watson, Mark W., 1989. "Interpreting the evidence on money-income causality," Journal of Econometrics, Elsevier, vol. 40(1), pages 161-181, January.
  9. 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.
  10. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
  11. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  12. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  13. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
  14. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  15. 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.
  16. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  17. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  18. 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.
  19. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  20. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
  21. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  22. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  23. 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).
  24. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
  25. 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.
  26. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  27. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
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