Multivariate Portmanteau test for Autoregressive models with uncorrelated but nonindependent errors

Christian Francq (1) , Hamdi Raïssi (2)

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we consider estimation and test of fit for multiple autoregressive time series models with nonindependent innovations. We derive the asymptotic distribution of the residual autocorrelations. It is shown that this asymptotic distribution can be quite different for models with iid innovations and models in which the innovations exhibit conditional heteroscedasticity or other forms of dependence. Consequently, the usual chi-square distribution does not provide adequate approximation to the distribution of the Box-Pierce goodness-of-fit portmanteau test in the presence of nonindependent innovations. We then 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.

Mots clés: Box-Pierce and Ljung-Box portmanteau tests; Vector weak AR model; Goodness-of-fit test; Residual autocorrelation; Diagnostic Checking; Box-Pierce and Ljung-Box portmanteau tests.

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]

Christian Francq, Hamdi Raïssi. Multivariate Portmanteau test for Autoregressive models with uncorrelated but nonindependent errors. Journal of Time Series Analysis, 2007, 28, pp.454-470. ⟨hal-00517078⟩