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Robust estimates for ARMA models

By N. Muler, D. Peña and V. J. Yohai


One of the most successful approaches for robust estimation of ARMA models is based on the robust filter introduced by Masreliez (1975). This approach was used in Denby and Martin (1979), Martin (1979), Martin et al. (1983) and Bianco et al. (1996). The advantage of using a robust filter is that it allows computing the innovations avoiding the propagation of the effect of previous outliers. This property is specially important when working with ARMA(p, q) models with q> 0 or when q = 0 and p is large. However, we can mention two shortcoming of this approach. The first one is that the resulting estimates are asymptotically biased. The second one is that there is not an asymptotic theory for these estimators, and therefore it is not possible to make inference. In this talk we propose a new class of robust estimates for ARMA models. To improve robustness the residual innovations are generated using a modified ARMA model where the effect of one innovation on the subsequent periods is bounded. The proposed estimates are a generalization of the MM-estimates introduced by Yohai (1987) for regression. An stationary and invertible ARMA model can be represented by φ(B)yt = θ(B)at + c where at is a white noise process, φ(B) and θ(B) are polinomials of the form φ(B) = 1−φ1B −...−φpB p and θ(B) = 1 − θ1B −... − θqB q with roots outside the unit circle. Let λ(B) = φ −1 (B)θ(B)

Topics: robust estimates, ARMA models
Year: 2013
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