Whittle estimator for finite-variance non-Gaussian time series with long memory

• 成果类型: Article
• 署名作者: Giraitis, L; Taqqu, MS
• 署名单位: Boston University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 178-203
• 关键词: CENTRAL LIMIT-THEOREMS; bivariate appell polynomials; Empirical Process; range dependence; quadratic-forms; Moving averages; functionals; parameter; CONVERGENCE; FIELDS

摘要

We consider time series Y-t = G(X-t) where X-t is Gaussian with long memory and G is a polynomial. The series Y-t may or may not have long memory. The spectral density g(theta)(x) of Y-t is parameterized by a vector theta and we want to estimate its true value theta(0). We use a least-squares Whittle-type estimator <(theta)over cap>(N) for theta(0), based on observations Y-1,...,Y-N. If Y-t is Gaussian, then root N(<(theta)over cap>(N)-theta(0)) converges to a Gaussian distribution. We show that for non-Gaussian time series Y-t, this root N consistency of the Whittle estimator does not always hold and that the limit is not necessarily Gaussian. This can happen even if Y-t has short memory.