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The Bierens test for certain nonstationary models

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  • Kasparis, Ioannis
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    Abstract

    We adapt the Bierens (1990) test to the I-regular models of Park and Phillips (2001). Bierens (1990) defines the test hypothesis in terms of a conditional moment condition. Under the null hypothesis, the moment condition holds with probability one. The probability measure used is that induced by the variables in the model, that are assumed to be strictly stationary. Our framework is nonstationary and this approach is not always applicable. We show that the Lebesgue measure can be used instead in a meaningful way. The resultant test is consistent against all I-regular alternatives.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 158 (2010)
    Issue (Month): 2 (October)
    Pages: 221-230

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    Handle: RePEc:eee:econom:v:158:y:2010:i:2:p:221-230

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

    Related research

    Keywords: Bierens test Consistent test Functional form misspecification Integrable models Local time Nonlinear cointegration Test of functional form Predictability of stock returns Unit root;

    References

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    1. 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.
    2. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    3. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    4. de Jong, Robert M., 2004. "Addendum To," Econometric Theory, Cambridge University Press, vol. 20(03), pages 627-635, June.
    5. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
    6. 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.
    7. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    8. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    9. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
    10. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
    11. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    12. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
    13. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    14. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
    15. Bierens, H.J., 1986. "Armax model specification testing, with an application to unemployment in the Netherlands," Serie Research Memoranda 0026, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    16. Bierens, Herman J., 1988. "ARMA Memory Index Modeling of Economic Time Series," Econometric Theory, Cambridge University Press, vol. 4(01), pages 35-59, April.
    17. de Jong, Robert & Wang, Chien-Ho, 2005. "Further Results On The Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 21(02), pages 413-430, April.
    18. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
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    Cited by:
    1. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
    2. Ioannis Kasparis & Peter C. B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," University of Cyprus Working Papers in Economics 2-2009, University of Cyprus Department of Economics.
    3. Chaohua Dong & Jiti Gao, 2012. "Specification Testing Driven by Orthogonal Series in Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 20/12, Monash University, Department of Econometrics and Business Statistics.
    4. Andreou, Elena & Kasparis, Ioannis & Phillips, Peter C. B., 2013. "Nonparametric Predictive Regression," CEPR Discussion Papers 9570, C.E.P.R. Discussion Papers.

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