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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.

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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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Find related papers by JEL classification:
  • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

References listed on IDEAS
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  1. 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.
  2. 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.
  3. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
  4. repec:att:wimass:9520 is not listed on IDEAS
  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. 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.
  7. 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.
  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.
  9. 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.
  10. 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.
  11. 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.
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Cited by:

  1. 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.
  2. 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.
  3. 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.
  4. Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  5. 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.
  6. 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.
  7. 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.
  8. Lavergne, Pascal & Patilea, Valentin, 2011. "One for all and all for one: regression checks with many regressors," MPRA Paper 35779, University Library of Munich, Germany.
  9. 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.
  10. 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.
  11. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
  12. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
  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. repec:wyi:journl:002120 is not listed on IDEAS
  15. 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.
  16. Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.
  17. 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.
  18. Zhu, Ke, 2015. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," MPRA Paper 61930, University Library of Munich, Germany.

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