Center-outward Rank- and Sign-based VARMA Portmanteau Tests
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Revisiting the pseudo-Gaussian tests of Chitturi (1974), Hosking (1980), and Li and McLeod (1981) for VARMA models from a Le Cam perspective, we first provide a more precise and rigorous description of the asymptotic behavior of the multivariate portmanteau test statistic. Then, based on the concepts of center-outward ranks and signs recently developed in Hallin et al. (2021), we propose a class of multivariate portmanteau rank- and sign-based test statistics which, under the null hypothesis and under a broad family of innovation densities, can be approximated by an asymptotically chi-square variable. The asymptotic properties of these tests are derived; simulations demonstrate their advantages over their classical pseudo-Gaussian counterpart.
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