Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms
We consider portmanteau tests for testing the adequacy of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, and allow to cover linear representations of general nonlinear processes. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) or the least squared estimator (LSE) and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung-Box (or Box-Pierce) portmanteau statistics for VARMA models with nonindependent innovations. In the standard framework (i.e. under iid assumptions on the noise), it is known that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables. The asymptotic distribution can be quite different when the independence assumption is relaxed. Consequently, the usual chi-squared distribution does not provide an adequate approximation to the distribution of the Box-Pierce goodness-of fit portmanteau test. 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.
|Date of creation:||07 Dec 2009|
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- 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.
- Boubacar Mainassara, Yacouba & Francq, Christian, 2009. "Estimating structural VARMA models with uncorrelated but non-independent error terms," MPRA Paper 15141, University Library of Munich, Germany.
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- 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.
- 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.
- Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL. Full references (including those not matched with items on IDEAS)
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