Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error termsReport as inadecuate




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* Corresponding author 1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie

Abstract : We consider portmanteau tests for testing the adequacy of structural vector autoregressive moving-average VARMA models under the assumption that the errors are uncorrelated but not necessarily independent. The structural forms are mainly used in econometrics to introduce instantaneous relationships between economic variables. We first study the joint distribution of the quasi-maximum likelihood estimator QMLE 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 in this framework. It is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables, which can be quite different from the usual chi-squared approximation used under independent and identically distributed iid assumptions on the noise. 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.

Keywords : weak VARMA models Goodness-of-fit test QMLE-LSE Box-Pierce and Ljung-Box portmanteau tests residual autocorrelation Structural representation weak VARMA models.





Author: Yacouba Boubacar Mainassara -

Source: https://hal.archives-ouvertes.fr/



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