The Annals of Statistics

Robust estimation for ARMA models

Nora Muler, Daniel Peña, and Víctor J. Yohai

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This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard M-estimates and to estimates based on a diagnostic procedure.

Article information

Ann. Statist., Volume 37, Number 2 (2009), 816-840.

First available in Project Euclid: 10 March 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F35: Robustness and adaptive procedures 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

MM-estimates outliers time series


Muler, Nora; Peña, Daniel; Yohai, Víctor J. Robust estimation for ARMA models. Ann. Statist. 37 (2009), no. 2, 816--840. doi:10.1214/07-AOS570.

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