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Distribution Free Goodness-of-Fit Tests for Linear Processes

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  • Miguel A. Delgado
  • Javier Hidalgo
  • Carlos Velasco

Abstract

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett's Tp-process with estimated parameters, which converges in distribution to the standard Brownian Motion under the null hypothesis. We discuss tests of different nature such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.

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File URL: http://sticerd.lse.ac.uk/dps/em/em482.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/482.

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Date of creation: Jan 2005
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Handle: RePEc:cep:stiecm:/2005/482

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Nonparametric model checking; spectral distribution; linear processes; martingale decomposition; local alternatives; omnibus; smooth and directional tests; long-range alternatives;

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References

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  1. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series /2001/424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  4. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
  5. L Giraitis & J Hidalgo & Peter M. Robinson, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
  6. Nikabadze, A. & Stute, W., 1997. "Model checks under random censorship," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 249-259, March.
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Citations

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Cited by:
  1. Tommaso, Proietti & Alessandra, Luati, 2012. "The Generalised Autocovariance Function," MPRA Paper 43711, University Library of Munich, Germany.
  2. Javier Hidalgo, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
  3. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
  4. 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.
  5. Guay, Alain & Guerre, Emmanuel & Lazarová, Štěpána, 2013. "Robust adaptive rate-optimal testing for the white noise hypothesis," Journal of Econometrics, Elsevier, vol. 176(2), pages 134-145.
  6. Delgado, Miguel A. & Velasco, Carlos, 2010. "Distribution-free tests for time series models specification," Journal of Econometrics, Elsevier, vol. 155(2), pages 128-137, April.
  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.
  8. Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.
  9. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 219-261.
  10. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
  11. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
  12. Javier Hidalgo, 2005. "Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole," STICERD - Econometrics Paper Series /2005/481, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  13. 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.
  14. Miguel A. Delgado & Carlos Velasco, 2007. "A new class of distribution-free tests for time series models specification," Economics Working Papers we078047, Universidad Carlos III, Departamento de Economía.
  15. Hidalgo, J., 2008. "Specification testing for regression models with dependent data," Journal of Econometrics, Elsevier, vol. 143(1), pages 143-165, March.
  16. Miguel A. Delgado & Carlos Velasco, 2010. "A distribution-free transform of the residuals sample autocorrelations with application to model checking," Economics Working Papers we101707, Universidad Carlos III, Departamento de Economía.
  17. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 361-411, September.

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