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

TL;DR

This paper revisits classical portmanteau tests for VARMA models from a Le Cam perspective and introduces new multivariate rank- and sign-based tests with improved asymptotic properties and practical advantages.

Contribution

It provides a rigorous asymptotic analysis of existing tests and proposes novel rank- and sign-based portmanteau tests for VARMA models.

Findings

New tests are asymptotically chi-square distributed under the null hypothesis.

Simulations show the new tests outperform classical pseudo-Gaussian tests.

Theoretical analysis clarifies the asymptotic behavior of multivariate portmanteau statistics.

Abstract

The pseudo-Gaussian portmanteau tests of Chitturi, Hosking, and Li and McLeod for VARMA models are revisited from a Le Cam perspective, providing a precise and more rigorous description of the asymptotic behavior of the multivariate portmanteau test statistic, which depends on the dimension $d$ of the observations, the number $m$ of lags involved, and the length $n$ of the observation period. Then, based on the concepts of center-outward ranks and signs recently developed (Hallin, del Barrio, Cuesta-Albertos, and Matr\' an, {\it Annals of Statistics} 49, 1139--1165, 2021), a class of multivariate rank- and sign-based portmanteau test statistics is proposed 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.