A weighted U-statistic based change point test for multivariate time series

• Published in: Statistical papers (Berlin, Germany) Vol. 64; no. 3; pp. 753 - 778
• Main Authors: Hu, Junwei, Wang, Lihong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2023; Springer Nature B.V
• Subjects: Asymptotic properties; Data analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Hypotheses; Insurance; Kernel functions; Management; Mathematics and Statistics; Multivariate analysis; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Regular Article; Simulation; Statistics; Statistics for Business; Time series; Weighting functions; 62H15; 62F40; 62E20; Bootstrap method; Weighted Brownian bridge; Weighted U-statistic; Change point test
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-022-01341-9

In this paper we study the change point detection for the mean of multivariate time series. We construct the weighted U-statistic change point tests based on the weight function
1
/
t
(
1
-
t
)
and some suitable kernel functions. We establish the asymptotic distribution of the test statistic under the null hypothesis and the consistency under the alternatives. A bootstrap procedure is applied to approximate the distribution of the test statistic and it is proved that the test statistic based on bootstrap sampling has the same asymptotic distribution as the original statistic. Numerical simulation and real data analysis show the good performance of the weighted change point test especially when the change point location is not in the middle of the observation period.