Estimação robusta de processos ARFIMA

Abstract

This document focus on the study of methodologies used for estimating the long memory parameter in ARFIMA processes contaminated by atypical data. The suggested methodologies are based on robust estimators for the spectrum of the process, which can be reasonablealternatives for the estimation of the fractional difference parameter in contaminated processes. The robust estimators of the spectrum are classified in two classes: M-estimators and L-estimators. In the former class, the robust estimator of the spectrum is a function of the square sum of the process Fourier coefficients. In the second class, the estimator demands the computing of a robust estimator for the autocovariance function, based on L-estimators (see, Ma & Genton (2000)). The computing of robust estimators for the spectrumof the process allows the development of semiparametric alternatives for estimating the memory parameter in contaminated ARFIMA processes (Fajardo et al. (2009)). The performance of the estimators is analyzed through Monte Carlo simulations and the results evidence the superiority of the M-estimators in practical applications. The robust estimatorsof the memory parameter can be considered as reasonable alternatives for estimating in ARFIMA processes contaminated by atypical data.