NONPARAMETRIC REGRESSION FOR LOCALLY STATIONARY TIME SERIES

• 成果类型: Article
• 署名作者: Vogt, Michael
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1043
• 发表日期: 2012
• 页码: 2601-2633
• 关键词: nonlinear autoregressive models; uniform-convergence rates; varying arch processes; geometric ergodicity; dependent data; NONSTATIONARY; inference

摘要

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suffer from the curse of dimensionality.