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Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models

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  • Escanciano, J. Carlos

Abstract

In this article we study a general class of goodness-of-fit tests for the conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; are consistent against a broad class of alternatives including Pitman's local alternatives converging at the parametric rate; and do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher order dependence, in particular to conditional heteroskedasticity of unknown form. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 101 (2006)
Issue (Month): (June)
Pages: 531-541

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Handle: RePEc:bes:jnlasa:v:101:y:2006:p:531-541

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References

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  1. 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.
  2. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(1), pages 143-176.
  3. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution free goodness-of-fit tests for linear processes," LSE Research Online Documents on Economics 6840, London School of Economics and Political Science, LSE Library.
  4. 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.
  5. 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.
  6. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
  7. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
  8. Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1065-1121, December.
  9. repec:att:wimass:9520 is not listed on IDEAS
  10. 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.
  11. 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.
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Citations

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Cited by:
  1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1030-1051, December.
  2. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
  3. Pascal Lavergne & Valentin Patilea, 2008. "One for All and All for One:Regression Checks With Many Regressors," Discussion Papers dp08-06, Department of Economics, Simon Fraser University.
  4. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
  5. 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.
  6. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series 1115, Economics, The University of Manchester.
  7. repec:wyi:journl:002120 is not listed on IDEAS
  8. Manuel A. Domínguez & Ignacio N. Lobato, 2006. "A Consistent Specification Test For Models Defined By Conditional Moment Restrictions," Economics Working Papers we064111, Universidad Carlos III, Departamento de Economía.
  9. 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.
  10. J. Carlos Escanciano & Carlos Velasco, 2010. "Specification tests of parametric dynamic conditional quantiles," Post-Print peer-00732534, HAL.
  11. Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra.
  12. Manuel Dominguez & Ignacio Lobato, 2010. "Consistent Inference in Models Defined by COnditional Moment Restrictions: an Alternative to GMM," Working Papers 1005, Centro de Investigacion Economica, ITAM.
  13. Manuel Vega-Gordillo & José Luis Álvarez-Arce, 2005. "Heterogeneity In Economic Freedom: Free Clusters Or Free Countries," Faculty Working Papers 08/05, School of Economics and Business Administration, University of Navarra.
  14. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
  15. 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.
  16. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(1), pages 125-147, February.
  17. Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.

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