点击次数：

论文类型：期刊论文

发表时间：2013-10-01

发表刊物：COMPUTATIONAL STATISTICS & DATA ANALYSIS

收录刊物：SCIE、EI、Scopus

卷号：66

页面范围：150-160

ISSN号：0167-9473

关键字：Partially linear model; Time series; Heteroscedasticity; Kernel; Simultaneous confidence bands

摘要：Partially linear models are extended linear models where one covariate is nonparametric, which is a good balance between flexibility and parsimony. The partially linear stochastic model with heteroscedastic errors is considered, where the nonparametric part can act as a trend. The estimators of the parametric component, the nonparametric component and the volatility function are proposed. Furthermore, simultaneous confidence bands about the nonparametric part and the volatility function are constructed based on their coverage probabilities, which are shown to be asymptotically correct. By the confidence bands, the problems of hypothesis testing in this model can be solved effectively from a global view. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies, and demonstrated by the analyses of non-stationary Australian annual temperature anomaly series and non-homoscedastic daily air quality measurements in New York, where the simultaneous confidence bands provide more comprehensive information about the nonparametric and volatility functions. (C) 2013 Elsevier B.V. All rights reserved.