Self-normalization Tests for Change Points in Functional Time Series

Music City Center 

Change point detection for functional time series has attracted considerable attention from researchers. Existing methods either rely on functional principle component analysis (FPCA), which may perform poorly with complex data, or use bootstrap approaches in forms that fall short in effectively detecting diverse types of changes. In our study, we propose a novel self-normalization (SN) test for functional time series implemented via a non-overlapping block bootstrap to circumvent the reliance on FPCA. The test statistic is a normalized cumulative sum (CUSUM) where the normalizing factor allows the capture of subtle local changes in the mean function. The theory contains the weak convergence and test consistency for both the original and the bootstrap versions of the test statistic. We further extend the test to detect changes in the lag-1 autocovariance operator. Simulation studies confirm the superior performance of our test across various settings, and real-world applications further illustrate its practical utility.

Change point detection

Functional time series

Self-normalization

Non-overlapping block bootstrap 

International Chinese Statistical Association