Inference for structural changes in nonstationary functional time series with partial measurement error
研究了一类局部平稳函数型时间序列中变化点的检测与定位问题，提出了不依赖预平滑和降维预处理的方法，适用于存在非平稳性、不连续轨迹和异质性部分测量误差的数据，并开发了R包fcpseed。
Abstract We study the problem of detecting and localizing change points for a general class of locally stationary functional time series. To accommodate the nonstationarity and other possible complex features, such as discontinuous trajectories, and heterogeneous partial measurement error of contemporary functional data, we propose methods that do not rest on the preprocessing techniques of presmoothing and dimension-reduction, which would be less accurate without the assumptions of stationarity and continuous trajectories. For detecting changes, we propose a bootstrap-assisted test for structural breaks among all mean trajectories, which is asymptotically correct and can detect local alternatives of n−1/2. For localizing changes, we develop practical and consistent algorithms for estimating single and multiple change points, which further enable the estimation of mean trajectories. To establish the theoretical properties of our approaches, we develop a new backward martingale difference inequality and a functional Burkholder inequality for nonstationary functional time series, which can be of independent interest. The effectiveness of our approach is demonstrated through extensive simulation studies and real data analyses. The proposed algorithms in this article are available in the R package fcpseed.