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

Junwei Hu and Lihong Wang ()
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Junwei Hu: Nanjing University
Lihong Wang: Nanjing University

Statistical Papers, 2023, vol. 64, issue 3, No 2, 753-778

Abstract: Abstract 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 $$1/{\sqrt{t(1-t)}}$$ 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.

Keywords: Bootstrap method; Change point test; Weighted Brownian bridge; Weighted U-statistic; 62H15; 62E20; 62F40 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01341-9

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