Abstract: For long range dependent time series with a spectral singularity at frequency zero, a theory for optimal bandwidth choice in non-parametric analysis of the singularity was developed by Robinson (1994a). In the present paper, the optimal bandwidths are compared with those in case of a smooth spectrum. They are also analysed in case of fractional ARIMA models and calculated as a function of the self similarity parameter in some special cases. Feasible data-dependent approximations to the optimal bandwidth are proposed. We also include some applications using real data.
Key words and phrases: Long range dependence, spectrum, self similarity parameter, semiparametric estimation, optimal bandwidth choice, ARFIMA models.