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Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives

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  • Jonathan B. Hill

Abstract

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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Bibliographic Info

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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Keywords: smooth transition models; consistent tests; nonlinearity; neural networks;

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  1. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, Elsevier, vol. 20(1), pages 105-134, October.
  2. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
  3. Corradi, V. & Swanson, N.R., 2000. "A Consistent Test for Nonlinear Out of Sample Predictive Accuracy," Discussion Papers, Exeter University, Department of Economics 0012, Exeter University, Department of Economics.
  4. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1383-1414, November.
  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, Elsevier, vol. 56(3), pages 269-290, April.
  6. 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).
  7. Skalin, Joakim, 1998. "Testing linearity against smooth transition autoregression using a parametric bootstrap," Working Paper Series in Economics and Finance 276, Stockholm School of Economics, revised 13 Dec 1998.
  8. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
  9. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(03), pages 295-325, June.
  10. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  11. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1133-59, September.
  12. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, Elsevier, vol. 75(2), pages 263-289, December.
  13. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  14. Phillip Rothman & Dick van Dijk & Philip Hans Franses, 2000. "A Multivariate STAR Analysis of the Relationship Between Money and Output," Working Papers, East Carolina University, Department of Economics 0012, East Carolina University, Department of Economics.
  15. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, Elsevier, vol. 47(1), pages 5-46, January.
  16. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  17. Alvaro Escribano & Oscar Jorda, . "Improved Testing And Specification Of Smooth Transition Regression Models," Department of Economics, California Davis - Department of Economics 97-26, California Davis - Department of Economics.
  18. van Dijk, D.J.C. & Franses, Ph.H.B.F., 1997. "Modelling Multiple Regimes in the Business Cycle," Econometric Institute Research Papers EI 9734/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  19. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 72(1-2), pages 1-32.
  20. Stock, James H. & Watson, Mark W., 1989. "Interpreting the evidence on money-income causality," Journal of Econometrics, Elsevier, Elsevier, vol. 40(1), pages 161-181, January.
  21. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1129-1152, September.
  22. Friedman, Benjamin M & Kuttner, Kenneth N, 1992. "Money, Income, Prices, and Interest Rates," American Economic Review, American Economic Association, American Economic Association, vol. 82(3), pages 472-92, June.
  23. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 26(3), pages 323-353, December.
  24. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 8(04), pages 435-451, December.
  25. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 484-489, June.
  26. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 1047-70, September.
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