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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.

Suggested Citation

  • Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series 482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:482
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    References listed on IDEAS

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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, November.
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    6. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series 424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, November.
    8. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    9. Nikabadze, A. & Stute, W., 1997. "Model checks under random censorship," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 249-259, March.
    10. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
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    Citations

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    Cited by:

    1. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2017. "Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas," Discussion Paper 2017-052, Tilburg University, Center for Economic Research.
    2. Hidalgo, J., 2008. "Specification testing for regression models with dependent data," Journal of Econometrics, Elsevier, vol. 143(1), pages 143-165, March.
    3. 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.
    4. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
    5. Komarova, Tatiana & Hidalgo, Javier, 2023. "Testing nonparametric shape restrictions," LSE Research Online Documents on Economics 121410, London School of Economics and Political Science, LSE Library.
    6. Javier Hidalgo & Myung Hwan Seo, 2013. "Specification For Lattice Processes," STICERD - Econometrics Paper Series 562, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Javier Hidalgo, 2007. "Specification Testing Forregression Models Withdependent Data," STICERD - Econometrics Paper Series 518, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. Chung, EunYi & Olivares, Mauricio, 2021. "Permutation test for heterogeneous treatment effects with a nuisance parameter," Journal of Econometrics, Elsevier, vol. 225(2), pages 148-174.
    9. Hidalgo, Javier, 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.
    10. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    11. Hidalgo, Javier & Zaffaroni, Paolo, 2007. "A goodness-of-fit test for ARCH([infinity]) models," Journal of Econometrics, Elsevier, vol. 141(2), pages 973-1013, December.
    12. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
    13. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    14. Sami Umut Can & John H. J. Einmahl & Roger J. A. Laeven, 2024. "Two-Sample Testing for Tail Copulas with an Application to Equity Indices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(1), pages 147-159, January.
    15. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.
    16. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2020. "Goodness-of-fit testing for copulas: A distribution-free approach," Other publications TiSEM 211b2be9-b46e-41e2-9b95-1, Tilburg University, School of Economics and Management.
    17. Delgado, Miguel A. & Velasco, Carlos, 2007. "A new class of distribution-free tests for time series models specification," UC3M Working papers. Economics we078047, Universidad Carlos III de Madrid. Departamento de Economía.
    18. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    19. Delgado, Miguel A. & Arteaga-Molina, Luis A., 2021. "Testing constancy in varying coefficient models," Journal of Econometrics, Elsevier, vol. 222(1), pages 625-644.
    20. 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.
    21. Hill, Jonathan B. & Motegi, Kaiji, 2019. "Testing the white noise hypothesis of stock returns," Economic Modelling, Elsevier, vol. 76(C), pages 231-242.
    22. 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.
    23. Delgado, Miguel A. & Velasco, Carlos, 2010. "A distribution-free transform of the residuals sample autocorrelations with application to model checking," UC3M Working papers. Economics we101707, Universidad Carlos III de Madrid. Departamento de Economía.
    24. Philip Preuss & Mathias Vetter & Holger Dette, 2013. "Testing Semiparametric Hypotheses in Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 417-437, September.

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    More about this item

    Keywords

    Nonparametric model checking; spectral distribution; linear processes; martingale decomposition; local alternatives; omnibus; smooth and directional tests; long-range alternatives;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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