An adaptive broadband estimator of the fractional differencing coefficient

We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially nonstationary linear long-memory time series with smooth additive trend. We use differencing to annihilate the trend, followed by tapering to handle the potential non-invertibility of the differenced series. We propose a method of pooling the tapered periodogram which leads to more efficient estimators of d than existing pooled, tapered estimators. We establish asymptotic normality of the estimator. Finally, we consider minimax rate-optimality and feasible nearly rate-optimal estimators. Some simulations are presented to illustrate our findings.