DETECTING GRADUAL CHANGES IN LOCALLY STATIONARY PROCESSES

• 成果类型: Article
• 署名作者: Vogt, Michael; Dette, Holger
• 署名单位: University of Konstanz; Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1297
• 发表日期: 2015
• 页码: 713-740
• 关键词: varying arch processes; time-series models; change-point; Nonparametric Regression; statistical-inference; threshold estimation; control charts; linear trend; settings

摘要

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows us to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher moments. The theoretical part of the paper establishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by two applications to financial return data.