Optimal spectral bandwidth for long memory

Abstract

For long range dependent time series with a spectral singularity at frequency zero, a theory for optimal bandwidth choice in non-parametric analysis ofthe singularity was developed by Robinson (1991b). The optimal bandwidths are described and compared with those in case of analysis 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 discussed.