ESTIMATION OF SEMIVARYING COEFFICIENT TIME SERIES MODELS WITH ARMA ERRORS

• 成果类型: Article
• 署名作者: Lei, Huang; Xia, Yingcun; Qin, Xu
• 署名单位: Southwest Jiaotong University; National University of Singapore; University of Electronic Science & Technology of China
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1430
• 发表日期: 2016
• 页码: 1618-1660
• 关键词: Nonparametric regression; autocorrelated errors; AUTOREGRESSIVE MODELS; correlated errors; kernel regression; identification; likelihood; splines

摘要

Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood estimation, this paper investigates in details a semi-parametric autoregressive model with ARMA sequence of residuals. Asymptotic normality of the estimators is established, and a model selection procedure is proposed. Numerical examples are employed to illustrate the performance of the proposed estimation method and the necessity of incorporating the serial correlation in the residuals.