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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.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 28 (2007)
Issue (Month): 3 (05)
Pages: 454-470

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Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:454-470

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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Cited by:
  1. 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.
  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. 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.
  4. 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.

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