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Article overview
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Center-Outward R-Estimation for Semiparametric VARMA Models | | Marc Hallin
; Davide La Vecchia
; Hang Liu
; | | Date: |
18 Oct 2019 | | 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. | | Source: | arXiv, 1910.8442 | | Services: | Forum | Review | PDF | Favorites | |
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