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Robust Estimation in Vector Autoregressive Moving‐Average Models

Author

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  • Marta Garcia Ben
  • Elena J. Martinez
  • Victor J. Yohai

Abstract

Bustos and Yohai proposed a class of robust estimates for autoregressive moving‐average (ARMA) models based on residual autocovariances (RA estimates). In this paper an affine equivariant generalization of the RA estimates for vector ARMA processes is given. These estimates are asymptotically normal and, when the innovations have an elliptical distribution, their asymptotic covariance matrix differs only by a scalar factor from the covariance matrix corresponding to the maximum likelihood estimate. A Monte Carlo study confirms that the RA estimates are efficient under normal errors and robust when the sample contains outliers. A robust multivariate goodness‐of‐fit test based on the RA estimates is also obtained.

Suggested Citation

  • Marta Garcia Ben & Elena J. Martinez & Victor J. Yohai, 1999. "Robust Estimation in Vector Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(4), pages 381-399, July.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:4:p:381-399
    DOI: 10.1111/1467-9892.00144
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    Cited by:

    1. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    2. Pierre Duchesne, 2005. "Robust and powerful serial correlation tests with new robust estimates in ARX models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 49-81, January.
    3. Le Chang & Yanlin Shi, 2024. "A discussion on the robust vector autoregressive models: novel evidence from safe haven assets," Annals of Operations Research, Springer, vol. 339(3), pages 1725-1755, August.
    4. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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