Change-point detection for object-valued time series

Music City Center 

Abstract: Statistical analysis of object-valued data that reside in a metric space is gradually emerging as an important branch of functional data analysis in statistics. Notable examples include networks, distributions and covariance matrices. Many object-valued data are collected as a time series, such as yearly age-at-death distributions for countries in Europe and daily Pearson correlation matrices for several cryptocurrencies. In this talk I will introduce some recent work on change-point detection for these non-Euclidean time series. For single change-point detection, we introduce a sample splitting and self-normalization test statistic that only depends on pairwise distance between two random objects and involves less number of tuning parameters than existing counterparts. For multiple change-point detection, we combine the single-change point test with wild binary segmentation to estimate the number and location of change-points. Both asymptotic theory and numerical results will be presented to demonstrate the efficacy and versatility of our proposed procedures.

Non-Euclidean;

Sample splitting;

Self-normalization;

Structural break