A1838
Title: Inference for structural changes in nonstationary functional time series with partial measurement error
Authors: Lujia Bai - Ruhr University Bochum (China)
Qirui Hu - Shanghai University of Finance and Economics (China)
Weichi Wu - Tsinghua University, China (China) [presenting]
Abstract: Change point detection and localization for a general class of locally stationary functional time series is studied. To accommodate nonstationarity and other possible complex features, such as discontinuous trajectories and heterogeneous partial measurement error of contemporary functional data, methods are proposed that do not rely on pre-processing techniques of pre-smoothing and dimension reduction, which would be less accurate without the assumptions of stationarity and continuous trajectories. For detecting changes, a bootstrap-assisted test for structural breaks among all mean trajectories is proposed, which is asymptotically correct and can detect local alternatives of $n^{-1/2}$. For localizing changes, practical and consistent algorithms are developed for estimating single and multiple change points, which further enable the estimation of mean trajectories. To establish the theoretical properties of the proposed approaches, a new backward martingale difference inequality and a functional Burkholder inequality for nonstationary functional time series are developed, which can be of independent interest. The effectiveness of the approach is demonstrated through extensive simulation studies and real data analyses. The proposed algorithms are available in the R package fcpseed.
