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Distribution Free Goodness-of-Fit Tests for Linear Processes

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Author Info
Miguel A. Delgado
Javier Hidalgo
Carlos Velasco

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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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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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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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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July. [Downloadable!] (restricted)
  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 and Swedish Statistical Association, vol. 27(1), pages 143-176. [Downloadable!] (restricted)
  3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
  5. Nikabadze, A. & Stute, W., 1997. "Model checks under random censorship," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 249-259, March. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
    Other versions:
  2. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series /2005/486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
  4. 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. [Downloadable!]
  5. 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. [Downloadable!]
    Other versions:
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