AUTOREGRESSIVE APPROXIMATIONS TO NONSTATIONARY TIME SERIES WITH INFERENCE AND APPLICATIONS

• 成果类型: Article
• 署名作者: Ding, Xiucai; Zhou, Zhou
• 署名单位: University of California System; University of California Davis; University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2288
• 发表日期: 2023
• 页码: 1207-1231
• 关键词: Nonparametric regression; Matrix Estimation; stationarity; covariance; rates; CONVERGENCE; models

摘要

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well ap-proximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a struc-tural approximation result is established for general classes of nonstationary time series. A high-dimensional L2 test and an associated multiplier boot-strap procedure are proposed for the inference of the AR approximation co-efficients. In particular, an adaptive stability test is proposed to check whether the AR approximation coefficients are time-varying, a frequently encountered question for practitioners and researchers of time series. As an application, globally optimal sffollowing hort-term forecasting theory and methodology for a wide class of locally stationary time series are established via the method of sieves.