B1382
Title: Testing and estimation of first-order structural changes in locally stationary functional time series
Authors: Lujia Bai - Tsinghua University (China) [presenting]
Qirui Hu - Tsinghua University (China)
Weichi Wu - Tsinghua University (China)
Abstract: Functional time series is an emerging research area that models dependent sequential, random functions drawn from infinite-dimensional spaces. However, the dependent structure in modern large time series datasets is often time-varying, leading to nonstationarity. As a result, accurately estimating and inferring changes in nonstationary functional time series is crucial to capturing and understanding the changing dynamics of their complex data-generating mechanisms. A CUSUM-based test is proposed for detecting changes in the functional mean and a wild binary segmentation approach for localizing multiple changes. A novel, consistent bootstrap procedure is introduced for the test and a new criterion for selecting the threshold for wild binary segmentation is adapted to the dependence and nonstationarity among functional objects, as well as possible measurement error when sampling random functions. Notably, it is demonstrated that the test can detect local alternatives at a rate of sqrt root n, and the estimation of change points achieves the rate of changing magnitude over n, similar to the best estimation accuracy for changes in univariate time series. The effectiveness of the method is shown using extensive simulation studies and real data analysis.
