February 2023 Rank-based testing for semiparametric VAR models: A measure transportation approach
Marc Hallin, Davide La Vecchia, Hang Liu
Author Affiliations +
Bernoulli 29(1): 229-273 (February 2023). DOI: 10.3150/21-BEJ1456

Abstract

We develop a class of tests for semiparametric vector autoregressive (VAR) models with unspecified innovation densities based on the recent measure-transportation-based concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam’s asymptotic theory of statistical experiments, yield novel testing procedures, which (a) are valid under a broad class of innovation densities (possibly non-elliptical, skewed, and/or with infinite moments), (b) are optimal (locally asymptotically maximin or most stringent) at selected ones, and (c) are robust against additive outliers. In order to show this, we establish, for a general class of center-outward rank-based serial statistics, a Hájek asymptotic representation result, of independent interest, which allows for a rank-based reconstruction of central sequences. As an illustration, we consider the problems of testing the absence of serial correlation in multiple-output and possibly non-linear regression (an extension of the classical Durbin-Watson problem) and the sequential identification of the order p of a VAR(p) model. A Monte Carlo comparative study of our tests and their routinely-applied Gaussian competitors demonstrates the benefits (in terms of size, power, and robustness) of our methodology; these benefits are particularly significant in the presence of asymmetric and leptokurtic innovation densities. A real-data application concludes the paper.

Acknowledgements

Following the mathematical tradition, the authors of this paper are listed alphabetically, meaning that they all are “first authors.” [Added upon request from the University of Science and Technology of China].

Citation

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Marc Hallin. Davide La Vecchia. Hang Liu. "Rank-based testing for semiparametric VAR models: A measure transportation approach." Bernoulli 29 (1) 229 - 273, February 2023. https://doi.org/10.3150/21-BEJ1456

Information

Received: 1 December 2020; Published: February 2023
First available in Project Euclid: 13 October 2022

MathSciNet: MR4497246
zbMATH: 07634391
Digital Object Identifier: 10.3150/21-BEJ1456

Keywords: distribution-freeness , Durbin-Watson test , Hájek representation , local asymptotic normality , multivariate ranks , VAR order selection

Vol.29 • No. 1 • February 2023
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