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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. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
    2. Bierens, Herman J., 1987. "Armax model specification testing, with an application to unemployment in the Netherlands," Journal of Econometrics, Elsevier, vol. 35(1), pages 161-190, May.
    3. Bierens, Herman J., 1988. "ARMA Memory Index Modeling of Economic Time Series," Econometric Theory, Cambridge University Press, vol. 4(01), pages 35-59, April.
    4. 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.
    5. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
    6. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
    7. 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.
    8. Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," Microeconomics.ca working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
    9. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
    10. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    11. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    12. 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.
    13. de Jong, Robert M., 2004. "Addendum To," Econometric Theory, Cambridge University Press, vol. 20(03), pages 627-635, June.
    14. 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.
    15. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    16. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
    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. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
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    Cited by:
    1. Ioannis Kasparis & Elena Andreou & Peter C. B. Phillips, 2012. "Nonparametric Predictive Regression," University of Cyprus Working Papers in Economics 14-2012, University of Cyprus Department of Economics.
    2. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    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. 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.

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