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Diagnostic checking of multivariate nonlinear time series models with martingale difference errors

  • Chabot-Hallé, Dominique
  • Duchesne, Pierre

In this article, we derive the asymptotic distribution of residual autocovariance and autocorrelation matrices for a general class of multivariate nonlinear time series models by assuming only that the error term is a martingale difference sequence. Two types of applications are developed: global test statistics of the portmanteau type and one-lag test statistics, which describe the residual correlation at individual lags. To illustrate the proposed methodology, simulation results are reported for diagnosing multivariate threshold time series models. The following test statistics are compared: the classical test statistics presuming independent errors and the proposed methodology which supposes only martingale difference errors.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 78 (2008)
Issue (Month): 8 (June)
Pages: 997-1005

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Handle: RePEc:eee:stapro:v:78:y:2008:i:8:p:997-1005
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  1. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  2. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  3. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
  4. Duchesne, Pierre, 2004. "On matricial measures of dependence in vector ARCH models with applications to diagnostic checking," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 149-160, June.
  5. Pierre Duchesne, 2005. "On the asymptotic distribution of residual autocovariances in VARX models with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 14(2), pages 449-473, December.
  6. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
  7. 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, 05.
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