Robust estimates for arch processes

Nora Muler and Victor J. Yohai

Journal of Time Series Analysis, 2002, vol. 23, issue 3, 341-375

Abstract: In this paper, we present two robust estimates for ARCH(p) models: τ ‐ and filtered τ‐estimates. These are defined by the minimization of conveniently robustified likelihood functions. The robustification is achieved by replacing the mean square error of the standardized observations with the square of a robust τ‐scale estimate in the reduced form of the Gaussian likelihood function. The robust filtering procedure avoids the propagation of the effect of one outlier on subsequent conditional variances. A Monte‐Carlo study shows that the maximum likelihood estimate practically collapses when there is only a small percentage of outlier contamination, while both robust estimates perform much better.

Date: 2002
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