Robust estimation in long-memory processes under additive outliers

Abstract

In this paper,we introduce an alternative semiparametric estimator of the fractional differencing parameter in ARFIMA models which is robust against additive outliers. The proposed estimator is a variant of the GPH estimator [Geweke,J.,Porter-Hudak,S.,1983.The estimation and application of long memory time series model. Journal of Time Serie Analysis 4,221–238]. In particular, we use the robusts ample autocorrelations of Ma, Y. and Genton,M.[2000.Highly robust estimation of the auto covariance function. Journal of Time Series Analysis 21,663–684] to obtain an estimator for the spectral density of the process .Numerical results show that the estimator we propose for the differencing parameter is robust when the data contain additive outliers.