MONITORING FOR A CHANGE POINT IN A SEQUENCE OF DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Horvath, Lajos; Kokoszka, Piotr; Wang, Shixuan
• 署名单位: Utah System of Higher Education; University of Utah; Colorado State University System; Colorado State University Fort Collins; University of Reading
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2036
• 发表日期: 2021
• 页码: 2271-2291
• 关键词: partial sums; tests; approximation; volatility; returns; models

摘要

We propose a method for the detection of a change point in a sequence {F-i} of distributions, which are available through a large number of observations at each i >= 1. Under the null hypothesis, the distributions F-i are equal. Under the alternative hypothesis, there is a change point i * > 1, such that F-i = G for i >= i* and some unknown distribution G, which is not equal to F-1. The change point, if it exists, is unknown, and the distributions before and after the potential change point are unknown. The decision about the existence of a change point is made sequentially, as new data arrive. At each time i, the count of observations, N, can increase to infinity. The detection procedure is based on a weighted version of the Wasserstein distance. Its asymptotic and finite sample validity is established. Its performance is illustrated by an application to returns on stocks in the S&P 500 index.