Estimation of the long memory parameter in nonstationary time series using semi-parametric and parametric methods

Abstract

Recently, the study of time series has been focused on time series having the long memory property, that is, series in which the dependence between distant observations is not negligible. One model that shows properties of long memory is the ARF IM A(p, d, q) 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(O,d*,O) processes when d* > 0.5, that is, when the processes are nonstationary, but still have the property of long memory. We present a study, through simulations, for the estimators of d* with different semiparametric and parametric methods for nonstationary processes when d* belongs to the intervals (0.5, 1.0) and (1.0,1.5).