COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1384

Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

Donald W.K. Andrews and Yixiao Sun

October 2002

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, , by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a "local polynomial Whittle" (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of  at zero and selects the bandwidth. The resulting "adaptive LPW" estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of  at zero, up to a logarithmic factor.

Keywords: Adaptive estimator, Asymptotic bias, Asymptotic normality, Bias reduction, Local polynomial, Long memory, Minimax rate, Optimal bandwidth, Whittle likelihood

JEL Classification Numbers: C13, C14, C22