Robust Inference for Nonstationary Time Series with Possibly Multiple Changing Periodic Structures
研究包含未知周期、非参数趋势和协变量效应的非平稳时间序列，提出两阶段估计方法处理可能变化的周期结构，并给出变点估计器，适用于全球变暖和中国进出口数据。
Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonparametric trending behavior and also additive covariate effects. Further, as the amplitude function may change at some known or unknown change-point(s), we extend our model to take this dynamical periodicity into account and introduce two change-point estimators. To the best of knowledge, this is the first work to study such complex periodic structure. A two-step estimation procedure is proposed to estimate accurately the periodicity, trend and covariate effects. First, we estimate the period with the trend and covariate effects being approximated by B-splines rather than being ignored. To achieve robustness we employ a penalized M-estimation method which uses post model selection inference ideas. Next, given the period estimate, we estimate the amplitude, trend and covariate effects. Asymptotic properties of our estimators are derived, including consistency of the period estimator and asymptotic normality and oracle property of the estimated periodic sequence, trend and covariate effects. Simulation studies confirm superiority of our method and illustrate good performance of our change-point estimators. Applications to the two motivating examples demonstrate utilities of our methods.