Inference for Locally Stationary Time Series Regression Models

• Activity Number: 90
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yeonwoo Rho*+ and Xiaofeng Shao
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: Dependent wild bootstrap ; Local stationarity ; Self-normalization ; Time series regression

Abstract

This paper is motivated by the need to assess the significance of the trend in the temperature series from the global warming studies, which exhibit certain degrees of nonstationarity. To capture the empirical features of the temperature series, we consider the linear regression model with a parametric trend function and locally stationary stochastic errors. The limiting distribution of the ordinary least squares estimator is asymptotically normal, but the asymptotic variance contains a number of nuisance parameters. To conduct the inference, we adopt the recently developed self-normalized approach and derive a functional central limit theorem for the recursive ordinary least squares estimators. The limiting distribution of the self-normalized statistic is non-pivotal but can be consistently approximated by using the dependent wild bootstrap. The consistency of the dependent wild bootstrap is rigorously justified in the locally stationary setting and the choice of the bandwidth parameter in the dependent wild bootstrap is also investigated through simulations.