Modified Schwarz and Hannan–Quinn information criteria for weak VARMA models
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Numerous multivariate time series admit weak vector autoregressive moving-average (VARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. These models are called weak VARMA by opposition to the standard VARMA models, also called strong VARMA models, in which the error terms are supposed to be independent and identically distributed (iid). This article considers the problem of order selection of the weak VARMA models by using the information criteria. It is shown that the use of the standard information criteria are often not justified when the iid assumption on the noise is relaxed. As a consequence, we propose the modified versions of the Schwarz or Bayesian information criterion and of the Hannan and Quinn criterion for identifying the orders of weak VARMA models. Monte Carlo experiments show that the proposed modified criteria estimate the model orders more accurately than the standard ones. An illustrative application using the squared daily returns of financial series is presented.
KeywordsIdentification Information criterion Order selection
Mathematics Subject ClassificationPrimary 62M10 91B84 Secondary 62H99
The research of the first author is supported by a BQR (Bonus Qualité Recherche) of the Université de Franche-Comté. We sincerely thank the associated editor and the anonymous reviewers for helpful remarks. Their detailed comments led to greatly improve the presentation.
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