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On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions

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  • Juan Carlos Escanciano

    ()
    (School of Economics and Business Administration, University of Navarra)

Abstract

Economic theories in dynamic contexts usually impose certain restrictions on the conditional mean of the underlying economic variables. Omnibus specification tests are the primary tools to test such restrictions when there is no information on the possible alternative. In this paper we study in detail the power properties of a large class of omnibus specification tests for parametric conditional means under time series processes. We show that all omnibus specification tests have a preference for a finite-dimensional space of alternatives (usually unknown to the practitioner) and we characterize such space for Cramér-von Mises (CvM) tests. This fact motivates the use of optimal tests against such preferred spaces instead of the omnibus tests. We proposed new asymptotically optimal directional and smooth tests that are optimally designed for cases in which a finite-dimensional space of alternatives is in mind. The new proposed optimal procedures are asymptotically distribution-free and are valid under weak assumptions on the underlying data generating process. In particular, they are valid under possibly time varying higher conditional moments of unknown form, e.g., conditional heteroskedasticity. A Monte Carlo experiment shows that previous asymptotic results provide good approximations in small sample sizes. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates the relevance of our results for practitioners.

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Bibliographic Info

Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 07/05.

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Length: 42 pages pages
Date of creation: May 2005
Date of revision:
Handle: RePEc:una:unccee:wp0705

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Web page: http://www.unav.es/facultad/econom

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References

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  1. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  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. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
  4. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  5. J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
  6. 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.
  7. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  8. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  9. repec:cup:etheor:v:8:y:1992:i:4:p:452-75 is not listed on IDEAS
  10. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
  11. 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.
  12. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  13. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  14. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
  15. Fong, Wai Mun & Ouliaris, Sam, 1995. "Spectral Tests of the Martingale Hypothesis for Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 255-71, July-Sept.
  16. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  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. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(04), pages 452-475, December.
  19. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
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Cited by:
  1. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.

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