An M-estimator for the long-memory parameter

• Published in: Journal of statistical planning and inference Vol. 187; pp. 44 - 55
• Main Authors: Reisen, V.A., Lévy-Leduc, C., Taqqu, M.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2017; Elsevier
• Subjects: [formula omitted]-estimation; Life Sciences; Long-memory; Outliers; Time series; Outliers; Long-memory; M-estimation; Time series
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2017.02.008

This paper proposes an M-estimator for the fractional parameter of stationary long-range dependent processes as an alternative to the classical GPH (Geweke and Porter-Hudak, 1983) method. Under very general assumptions on the long-range dependent process the consistency and the asymptotic normal distribution are established for the proposed method. One of the main results is that the convergence rate of the M-estimator is Nβ/2, for some positive β, which is the same rate as the standard GPH estimator. The asymptotic properties of the M-estimation method is investigated through Monte-Carlo simulations under the scenarios of ARFIMA models using contaminated with additive outliers and outlier-free data. The GPH approach is also considered in the study for comparison purposes, since this method is widely used in the literature of long-memory time series. The empirical investigation shows that M and GPH-estimator methods display standardized densities fairly close to the standard Gaussian density in the context of non-contaminated data. On the other hand, in the presence of additive outliers, the M-estimator remains unaffected with the presence of additive outliers while the GPH is totally corrupted, which was an expected performance of this estimator. Therefore, the M-estimator here proposed becomes an alternative method to estimate the long-memory parameter when dealing with long-memory time series with and without outliers. •We propose a novel estimator for the long-memory parameter.•It is an alternative to the classical GPH estimator.•It has the same asymptotic properties as the GPH estimator.•It is less sensitive to the presence of additive outliers in the data.