Center-outward Rank- and Sign-based VARMA Portmanteau Tests: Chitturi, Hosking, and Li–McLeod revisited

The pseudo-Gaussian portmanteau tests of Chitturi, Hosking, and Li McLeod for VARMA models are revisited from a Le Cam perspective, providing precise more rigorous description the asymptotic behavior multivariate test statistic, which depends on dimension d observations, number m lags involved, length n observation period. Then, based concepts center-outward ranks signs recently developed (Hallin, del Barrio, Cuesta-Albertos, Matrán, Annals Statistics 49, 1139–1165, 2021), class rank- sign-based statistics is proposed which, under null hypothesis broad family innovation densities, can be approximated by an asymptotically chi-square variable. properties these derived; simulations demonstrate their advantages over classical counterpart.