Adaptive Local Polynomial Whittle Estimation of Long-range Dependence
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, <formula format="inline"> <simplemath>ϕ(λ)</simplemath> </formula>, 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 <formula format="inline"> <simplemath>ϕ(λ)</simplemath> </formula> 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 <formula format="inline"> <simplemath>ϕ(λ)</simplemath> </formula> at zero, up to a logarithmic factor. Copyright The Econometric Society 2004.
