Adaptive local polynomial whittle estimation of long-range dependence

• 成果类型: Article
• 署名作者: Andrews, DWK; Sun, YX
• 署名单位: Yale University; University of California System; University of California San Diego
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2004.00501.x
• 发表日期: 2004
• 页码: 569-614
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS; LOG-PERIODOGRAM REGRESSION; semiparametric estimation; asymptotic properties; memory; parameter

摘要

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.