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

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 of the observations, the number of lags involved, and the length 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…
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Monetary Policy and Economic Impact · Forecasting Techniques and Applications
