Robust estimation in time series with long and short memory properties

This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and L\'evy-Leduc et al. (2011a), the emphasis in this paper is given in the following directions; the influence of additive outliers in the estimation of a time series, the asymptotic properties of a robust autocovariance function and a robust semiparametric estimation method of the fractional parameter d in ARFIMA(p, d, q) models. Some simulations are used to support the use of the robust method when a time series has additive outliers. The invariance property of the estimators for the first difference in ARFIMA model with outliers is also discussed. In general, the robust long-memory estimator leads to be outlier resistant and is invariant to first differencing.