Non-stationary Gaussian ARFIMA processes: Estimation and application

Recently, the study of time series turned the attention to the ones having long memory property. The ARFIMA (p,d,q) model shows this property when the degree of differencing d is in the interval (0.0,0.5), range where the process is stationary. In this work, we analyze the estimation of the degree d' " in ARFIMA (p,d' ",q) processes when d ">0.5, that is, when the processes are non-stationary but still have the property of long memory. We present a simulation study for the estimators of d * with semi parametric and parametric methods and different sample sizes. The methodology is applied to the experimental data series of UK long interest gilts. Resumo Recentes estudos em Series Temporais tern dado atenc;ao aquelas com pro priedade de Zonga dependencia. Os modelos ARFIMA (p,dJq) evidenciam esta propriedade quando 0 grau de diferenciac;ao d esta no intervalo (0.0,0.5), regiao onde 0 processo e estacionario. Neste trabalho, nos analisamos a estima�ao do parametro d' " em processos ARFIMA (p,d' ",q) quando d *>0.5, isto e, quando os processos sao nao-estaciomirios mas ainda possuem a propriedade de longa de pendencia. Apresentamos urn estudo de simulac;ao para estimadores de d' " com metodos semiparametricos e parametricos e diferentes tamanhos amostrais. A metodologia e aplicada para a serie temporal "UK long interest gilts "