An Efficient Taper for Potentially Overdifferenced Long-Memory Time Series

Abstract

We propose a new complex-valued taper and derive the properties of a tapered Gaussian semiparametric estimator of the long-memory parameter d є (-0.5, 1.5). The estimator and its accompanying theory can be applied to generalized unit root testing. In the proposed method, the data are differenced once before the taper is applied. This guarantees that the tapered estimator is invariant with respect to deterministic linear trends in the original series. Any detrimental leakage effects due to the potential noninvertibility of the differenced series are strongly mitigated by the taper. The proposed estimator is shown to be more efficient than existing invariant tapered estimators. Invariance to kth order polynomial trends can be attained by differencing the data k times and then applying a stronger taper, which is given by the kth power of the proposed taper. We show that this new family of tapers enjoys strong efficiency gains over comparable existing tapers. Analysis of both simulated and actual data highlights potential advantages of the tapered estimator of d compared with the nontapered estimator.

Keywords: Periodogram, Gaussian semiparametric estimation, unit roots