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Center-Outward R-Estimation for Semiparametric VARMA Models

Author

Listed:
  • Marc Hallin
  • Davide La Vecchia
  • H Liu

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.

Suggested Citation

  • Marc Hallin & Davide La Vecchia & H Liu, 2019. "Center-Outward R-Estimation for Semiparametric VARMA Models," Working Papers ECARES 2019-25, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/294809
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    Keywords

    Multivariate ranks; Distribution-freeness; Local asymptotic normality; Measure transportation; Quasi likelihood estimation; Skew innovation density;

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