Willa Chen (Texas A&M)

Efficiency in Estimation of Long Memory

The tapered Gaussian semiparametric estimator (GSE) and, more recently, the exact local (ELW) Whittle estimator are two major approaches in estimating the memory parameter d of a potential nonstationary/noninvertible process. Though the ELW estimator has uniform efficiency for all values of d, it pays a much higher computational cost. On the other hand, the tapered GSE has the trend invariant property and computational advantage, but the variance of estimates increases with the order of tapers. We introduce a class of shift invariant tapers and study the efficient properties of the new tapered GSE. These tapers, which are of orders (p,q), are a maximally efficient sub-class of tapers originally proposed by Chen (2001). If the choice of q=n^{kapa/2p}, a taper is also of degree (p,kapa) defined by Dahlhaus (1988). We investigate whether/how the new tapered GSE can reach the same efficiency as the non-tapered GSE for d in the range of (-0.5,0.5), i.e. a limiting distribution of! N(0,1/4). Furthermore, we conduct a simulation study to compare finite sample properties of the new tapered GSE with those of the ELW (Shimotsu & Phillips, 2005), specifically the modified version by Shimotsu (2005), the two-step feasible ELW estimation. With a tapered GSE estimate as the initial value, this modified version of ELW can be applied to a nonstationary process with unknown mean and trend and is asymptotically N(0,1/4), though it does not have the mean or trend invariant property and the same computational efficiency as the tapered GSE.