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Model Checks Using Residual Marked Empirical Processes

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Author Info
Juan Carlos Escanciano () (School of Economics and Business Administration, University of Navarra)

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Abstract

This paper proposes omnibus and directional tests for testing the goodness-of-fit of a parametric regression time series model. We use a general class of residual marked empirical processes as the building-blocks for estimation and testing of such models. First, we establish a weak convergence theorem under mild assumptions, which allows us to study in a unified way the asymptotic null distribution of the test statistics and their asymptotic behavior against Pitman's local alternatives. To approximate the asymptotic null distribution of test statistics we justify theoretically a bootstrap procedure. Also, some asymptotic theory for the estimation of the principal components of the residual marked processes is considered. This asymptotic theory is used to derive optimal directional tests and efficient estimation of regression parameters. Finally, a Monte Carlo study shows that the bootstrap and the asymptotic results provide good approximations for small sample sizes and an empirical application to the Canadian lynx data set is considered.

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Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 13/04.

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Length: 44 pages pages
Date of creation: Sep 2004
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Publication status: Forthcoming, Statistica Sinica
Handle: RePEc:una:unccee:wp1304

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C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December. [Downloadable!]
  2. Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  3. repec:cup:etheor:v:8:y:1992:i:4:p:452-75 is not listed on IDEAS
  4. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February. [Downloadable!] (restricted)
  5. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness-of-fit test for time series," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678. [Downloadable!] (restricted)
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  6. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September. [Downloadable!] (restricted)
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  7. 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. [Downloadable!]
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  8. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  9. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin. [Downloadable!]
  10. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November. [Downloadable!] (restricted)
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  11. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June. [Downloadable!] (restricted)
  12. Winfried Stute, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 29(3), pages 535-545. [Downloadable!] (restricted)
  13. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
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  14. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December. [Downloadable!] (restricted)
  15. J. Franke & J.-P. Kreiss & E. Mammen, . "Bootstrap of kernel smoothing in nonlinear time series," Sonderforschungsbereich 373 1997-20, Humboldt Universitaet Berlin.
  16. 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. [Downloadable!]
  17. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August. [Downloadable!] (restricted)
  18. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  2. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  3. Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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