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Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors

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  • Christian Francq
  • Hamdi Raïssi

Abstract

We study the asymptotic behaviour of the least squares estimator, of the residual autocorrelations and of the Ljung-Box (or Box-Pierce) portmanteau test statistic for multiple autoregressive time series models with nonindependent innovations. Under mild assumptions, it is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, this asymptotic distribution can be quite different from that of models with independent and identically distributed innovations. Consequently, the usual chi-squared distribution does not provide an adequate approximation to the distribution of the Box-Pierce goodness-of-fit portmanteau test in the presence of nonindependent innovations. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte carlo experiments illustrate the finite sample performance of the modified portmanteau test. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Suggested Citation

  • Christian Francq & Hamdi Raïssi, 2007. "Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 454-470, May.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:454-470
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    Cited by:

    1. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    2. Boubacar Mainassara, Yacouba, 2010. "Selection of weak VARMA models by modified Akaike's information criteria," MPRA Paper 24981, University Library of Munich, Germany.
    3. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    4. Patilea, V. & Raïssi, H., 2013. "Corrected portmanteau tests for VAR models with time-varying variance," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 190-207.
    5. Pierre Duchesne & Pierre Lafaye de Micheaux, 2013. "Distributions for residual autocovariances in parsimonious periodic vector autoregressive models with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 496-507, July.
    6. Chabot-Hallé, Dominique & Duchesne, Pierre, 2008. "Diagnostic checking of multivariate nonlinear time series models with martingale difference errors," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 997-1005, June.
    7. Abdelkamel Alj & Christophe Ley & Guy Melard, 2015. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients: Part I," Working Papers ECARES ECARES 2015-21, ULB -- Universite Libre de Bruxelles.
    8. Boubacar Maïnassara, Yacouba & Raïssi, Hamdi, 2015. "Semi-strong linearity testing in linear models with dependent but uncorrelated errors," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 110-115.

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