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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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Related research

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

Find related papers by JEL classification:

• C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
• C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
• C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

This paper has been announced in the following NEP Reports:

• NEP-ALL-2004-10-30 (All new papers)
• NEP-ECM-2004-10-30 (Econometrics)
• NEP-ETS-2004-10-30 (Econometric Time Series)

References

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1. 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.
   
   • Corradi, V. & Swanson, N.R., 2000. "A Consistent Test for Nonlinear Out of Sample Predictive Accuracy," Discussion Papers 0012, Exeter University, Department of Economics.
2. 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.
3. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
4. 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.
   
   • Tom Doan, . "RATS programs to replicate Hansen's threshold estimation and testing results," Statistical Software Components RTZ00091, Boston College Department of Economics.
   • Tom Doan, . "TAR: RATS procedure to estimate a threshold autoregression, tests for threshold effect," Statistical Software Components RTS00209, Boston College Department of Economics.
   • 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).
5. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor and Francis Journals, vol. 21(1), pages 1-47.
   
   • Dijk, D.J.C. van & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Report EI 2000-23/A, Erasmus University Rotterdam, Econometric Institute.
   • 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.
6. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
7. 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.
   
   • Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
8. 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.
9. Rothman, P. & Dijk, D.J.C. van & Franses, Ph.H.B.F., 1999. "A multivariate STAR analysis of the relationship between money and output," Econometric Institute Report EI 9945-/A, Erasmus University Rotterdam, Econometric Institute.
   
   • 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.
   • Philip Rothman & Dick van Dijk & Philip Hans Franses, 1999. "A Multivariate STAR Analysis of the Relationship Between Money and Output," Working Papers 9913, East Carolina University, Department of Economics.
10. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    
    • Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
11. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
12. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    
    • Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
13. Oscar Jorda & Alvaro Escribano, 2003. "Improved Testing And Specification Of Smooth Transition Regression Models," Working Papers 9726, University of California, Davis, Department of Economics.
    
    • Alvaro Escribano & Oscar Jorda, . "Improved Testing And Specification Of Smooth Transition Regression Models," Department of Economics 97-26, California Davis - Department of Economics.
14. 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.
15. 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.
    
    • Tom Doan, . "REGRESET: RATS procedure to perform Ramsey RESET test on regression," Statistical Software Components RTS00181, Boston College Department of Economics.
    • Tom Doan, . "REGWHITENNTEST: RATS procedure to perform White neural network test on regression," Statistical Software Components RTS00183, Boston College Department of Economics.
16. 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.
17. 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.
18. 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.
19. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
20. 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.
21. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
22. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
23. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, 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, vol. 8(04), pages 435-451, December.
25. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.

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