Semiparametric estimation for stationary processes whose spectra have an unknown pole

• 成果类型: Article
• 署名作者: Hidalgo, J
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000318
• 发表日期: 2005
• 页码: 1843-1889
• 关键词: long-range dependence; time-series; memory; regression; inference; models

摘要

We consider the estimation of the location of the pole and memory parameter, lambda(0) and alpha, respectively, of covariance stationary linear processes whose spectral density function f(lambda) satisfies f(lambda) similar to C vertical bar lambda - lambda(0)vertical bar(-alpha) in a neighborhood of lambda(0). We define a consistent estimator of lambda(0) and derive its limit distribution Z(lambda)0. As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z(lambda 0) is distributed as a normal random variable when lambda(0) is an element of (0, pi), whereas for lambda(0) = 0 or pi, Z(lambda 0) is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when lambda(0) = 0, Z(lambda 0) is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a two-step estimator of the memory parameter alpha, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of lambda(0). Thus, we reinforce and extend previous results with respect to the estimation of alpha when lambda(0) is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators.