Robust estimation for ARMA models

TL;DR

This paper proposes a new class of robust M-estimates for ARMA models that limit the influence of outliers, are consistent, and have tractable asymptotic properties, showing improved performance in simulations.

Contribution

It introduces a novel robust estimation method for ARMA models with limited outlier influence and proven asymptotic consistency.

Findings

Robust estimates outperform standard M-estimates in simulations.

The proposed method has tractable asymptotic theory.

Estimates are consistent and effectively limit outlier impact.

Abstract

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.