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Robust estimation in vector autoregressive models based on a robust scale. (English) Zbl 1034.62082

Summary: A new class of robust estimates for vector autoregressive processes is proposed. The autoregressive coefficients and the covariance matrix of the innovations are estimated simultaneously by minimizing the determinant of the covariance matrix estimate, subject to a constraint on a robust scale of the Mahalanobis norms of the innovation residuals. By choosing as robust scale a \(\tau\)-estimate, the resulting estimates combine good robustness properties and asymptotic efficiency under Gaussian innovations. These estimates are asymptotically normal and in the case that the innovations have an elliptical distribution, their asymptotic covariance matrix differs only by a scalar factor from the one corresponding to the maximum likelihood estimate.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)
62F12 Asymptotic properties of parametric estimators
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