Local Whittle estimation of long memory: Standard versus bias-reducing techniques

Frequency domain semiparametric estimation of memory parameters belongs to the standard toolkit of applied time series researchers. These methods are based on a local approximation of the spectral density, which robustifies the estimation methods against misspecification, but induces a loss with respect to the parametric setting, where the spectral density is known up to a finite number of unknown parameters. In particular, standard semiparametric estimators have convergence rates no better than T2/5, whereas the rate T1/2 is achievable under parametric assumptions. Refinements of the local approximation have been developed by means of bias-reducing techniques, implying that rates arbitrarily close to the parametric one are achievable in the semiparametric setting. Two of these approaches to cover more general settings (including non-stationarity) are extended. A Monte Carlo experiment of finite sample performance is used to assess whether the asymptotic advantages of the bias-reducing methods materialize in better finite sample behavior.