Multivariate portmanteau tests for weak multiplicative seasonal VARMA models

  • Yacouba Boubacar MaïnassaraEmail author
  • Abdoulkarim Ilmi Amir
Regular Article


Numerous multivariate time series encountered in real applications display seasonal behavior. In this paper we consider portmanteau tests for testing the adequacy of structural multiplicative seasonal vector autoregressive moving-average (SVARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak SVARMA). We study the asymptotic distributions of residual autocorrelations at seasonal lags of multiple of the length of the seasonal period under weak assumptions on the noise. We deduce the asymptotic distribution of the proposed multivariate portmanteau statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. A set of Monte Carlo experiments and an application of U.S. monthly housing starts and housing sold are presented.


Goodness-of-fit test Quasi-maximum likelihood estimation Portmanteau tests Residual autocorrelation Weak SVARMA models 

Mathematics Subject Classification

Primary 62M10 62F03 62F05 Secondary 91B84 62P05 



We sincerely thank the anonymous reviewers and Editor for helpful remarks.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de mathématiques de BesançonUniversité Bourgogne Franche-Comté, UMR CNRS 6623BesançonFrance

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