A NOTE ON THE ESTIMATION OF DEGREE OF DIFFERENCING IN LONG MEMORY TIME SERIES ANALYSIS

Abstract. In this paper we investigate the properties of the estimator of degree of differencing the fractional d in long memory time series analysis via consistent spectral density estimation. It is shown that the proposed estimator is more eficient than some of the others in practice. I. Tntrredoctiors. The interest in fractional differencing and its applications to long memory time series modelling have become important to theoretical and applied time series analysis after the pioneering work by [ 5] and 161. Since then a large number of authors have reported some interesting and math-ematically elegant results on the modelling of long memory processes. This class of models is motivated by (i) unbounded spectral densities at the frequency o = 0, (ii) hyperbolic decay of the autocorrelation function (acf), and (iii) the Hurst effect. When modelling long memory time series, it is convenient to use the following two filters in tandem: (a) transform the original long memory {X,) to a short memory ( q) vi