Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations - Laboratoire de Mathématiques de Besançon (UMR 6623) Accéder directement au contenu
Article Dans Une Revue Journal of the American Statistical Association Année : 2018

Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations

Résumé

In this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving-average (VARMA) models with uncorrelated but non-independent innovations by using a self-normalization approach. We establish the asymptotic distribution of the proposed statistics. This asymptotic distribution is quite different from the usual chi-squared approximation used under the independent and identically distributed assumption on the noise, or the weighted sum of independent chi-squared random variables obtained under nonindependent innovations. A set of Monte Carlo experiments and an application to the daily returns of the CAC40 is presented.
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hal-04551949 , version 1 (18-04-2024)

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Yacouba Boubacar Maïnassara, Bruno Saussereau. Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations. Journal of the American Statistical Association, 2018, 113 (524), pp.1813-1827. ⟨10.1080/01621459.2017.1380030⟩. ⟨hal-04551949⟩
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