Bootstrapping locally stationary processes

• 成果类型: Article
• 署名作者: Kreiss, Jens-Peter; Paparoditis, Efstathios
• 署名单位: Braunschweig University of Technology; University of Cyprus
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12068
• 发表日期: 2015
• 页码: 267-290
• 关键词: Adaptive Estimation; models

摘要

We propose a non-parametric method to bootstrap locally stationary processes which combines a time domain wild bootstrap approach with a non-parametric frequency domain approach. The method generates pseudotime series which mimic (asymptotically) correct, the local second-and to the necessary extent the fourth-order moment structure of the underlying process. Thus it can be applied to approximate the distribution of several statistics that are based on observations of the locally stationary process. We prove a bootstrap central limit theorem for a general class of statistics that can be expressed as functionals of the preperiodogram, the latter being a useful tool for inferring properties of locally stationary processes. Some simulations and a real data example shed light on the finite sample properties and illustrate the ability of the bootstrap method proposed.