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Model Checks Using Residual Marked Empirical Processes

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  • Juan Carlos Escanciano

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

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.

Suggested Citation

  • 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.
  • Handle: RePEc:una:unccee:wp1304
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    File URL: http://www.unav.edu/documents/10174/6546776/1132582885_wp1304.pdf
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    References listed on IDEAS

    as
    1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    2. 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, August.
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    7. 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.
    8. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
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    18. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
    19. 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.
    20. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(5), pages 604-621, October.
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    Cited by:

    1. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    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. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
    4. Nedeljković, Milan & Urošević, Branko, 2012. "Determinants of the Dinar-Euro Nominal Exchange Rate," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 121-141, September.
    5. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.
    6. Leucht, Anne & Neumann, Michael H. & Kreiss, Jens-Peter, 2013. "A model specification test for GARCH(1,1) processes," Working Papers 13-11, University of Mannheim, Department of Economics.
    7. Milan Nedeljkovic & Branko Urosevic, 2011. "Determinants of the Dinar-Euro Nominal Exchange Rate," Working papers 18, National Bank of Serbia.
    8. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    9. Vanessa Berenguer Rico & Bent Nielsen, 2017. "Marked and Weighted Empirical Processes of Residuals with Applications to Robust Regressions," Economics Series Working Papers 841, University of Oxford, Department of Economics.
    10. James Davidson & Andreea G. Halunga, 2013. "Consistent Model Specification Testing," Discussion Papers 1312, University of Exeter, Department of Economics.
    11. 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.
    12. 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.

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    JEL classification:

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

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