Document Type
Discussion Paper
Publication Date
10-1-2002
CFDP Number
1384
CFDP Pages
50
Abstract
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.
Recommended Citation
Andrews, Donald W.K. and Sun, Yixiao, "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence" (2002). Cowles Foundation Discussion Papers. 1649.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1649