A robust method for shift detection in time series

• 成果类型: Article
• 署名作者: Dehling, H.; Fried, R.; Wendler, M.
• 署名单位: Ruhr University Bochum; Dortmund University of Technology; Otto von Guericke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa004
• 发表日期: 2020
• 页码: 647660
• 关键词: location; quantiles; variance; tests

摘要

We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.