Bandwidth Choice in Gaussian Semiparametric Estimation of Long Range Dependence

Abstract

We consider covariance stationary processes with spectral density which behaves according to a power law around zero frequency, where it can be infinite (long range dependence), finite and positive (short range dependence), or zero (antipersistence). This behaviour is governed by a self-similarity parameter which can be estimated semiparametrically by one of several methods, all of which require a choice of bandwidth. We consider a Gaussian estimate which seems likely to have good efficiency, and whose asymptotic distributional properties have already been determined. The minimum mean squared error optimal bandwidth is heuristically derived and feasible approximations to it are proposed, these being assessed in Monte Carlo experiments and applied to financial and Nile river data.