Center-outward R-estimation for semiparametric VARMA models

Hallin, Marc and La Vecchia, Davide and Liu, Hang (2019) Center-outward R-estimation for semiparametric VARMA models. Working Paper. Arxiv.

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Abstract

We propose a new class of estimators for semiparametric VARMA models with the innovation density playing the role of nuisance parameter. Our estimators are R-estimators based on the multivariate concepts of center-outward ranks and signs recently proposed by Hallin~(2017). We show how these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield a robust yet flexible and powerful class of estimation procedures for multivariate time series. We develop the relevant asymptotic theory of our R-estimators, establishing their root-n consistency and asymptotic normality under a broad class of innovation densities including, e.g., multimodal mixtures of Gaussians or and multivariate skew-t distributions. An implementation algorithm is provided in the supplementary material, available online. A Monte Carlo study compares our R-estimators with the routinely-applied Gaussian quasi-likelihood ones; the latter appear to be quite significantly outperformed away from elliptical innovations. Numerical results also provide evidence of considerable robustness gains. Two real data examples conclude the paper.

Item Type:
Monograph (Working Paper)
ID Code:
138920
Deposited By:
Deposited On:
13 Nov 2019 10:05
Refereed?:
No
Published?:
Published
Last Modified:
02 Jul 2020 07:26