CFDP 1384

Adaptive Local Polynomial Whittle Estimation of Long-range Dependence


Publication Date: October 2002

Pages: 50


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, φ(λ), 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 φ(λ) 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 φ(λ) at zero, up to a logarithmic factor.


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

JEL Classification Codes:  C13, C14, C22

See CFP: 1080