Adaptive Local Polynomial Whittle Estimation of Long-range Dependence by Donald

1 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.