Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence

51 Pages Posted: 4 Nov 2002

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics

Date Written: October 2002

Abstract

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Kunsch (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, phi (lambda), 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 phi (lambda) 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 phi (lambda ) 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: C13, C14, C22

Suggested Citation

Andrews, Donald W. K. and Sun, Yixiao, Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence (October 2002). Available at SSRN: https://ssrn.com/abstract=348163

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-4692 (Phone)
858-534-7040 (Fax)

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